Solve 22-(-14 6x-2 - 4^ 2 x-6-12 7^ 2 /8*3 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{22-(-14}{6x-2}-\frac{4^{2}x-6-12}{7^{2}\div8\times3}$$

Evaluate

$\frac{-384x^{2}+10262x-2349}{147\left(3x-1\right)}$

Short Solution Steps

Calculate $4$ to the power of $2$ and get $16$.

$$22-\frac{-14}{6x-2}-\frac{16x-6-12}{\frac{7^{2}}{8}\times 3}$$

Subtract $12$ from $-6$ to get $-18$.

$$22-\frac{-14}{6x-2}-\frac{16x-18}{\frac{7^{2}}{8}\times 3}$$

Calculate $7$ to the power of $2$ and get $49$.

$$22-\frac{-14}{6x-2}-\frac{16x-18}{\frac{49}{8}\times 3}$$

Express $\frac{49}{8}\times 3$ as a single fraction.

$$22-\frac{-14}{6x-2}-\frac{16x-18}{\frac{49\times 3}{8}}$$

Multiply $49$ and $3$ to get $147$.

$$22-\frac{-14}{6x-2}-\frac{16x-18}{\frac{147}{8}}$$

Divide $16x-18$ by $\frac{147}{8}$ by multiplying $16x-18$ by the reciprocal of $\frac{147}{8}$.

$$22-\frac{-14}{6x-2}-\frac{\left(16x-18\right)\times 8}{147}$$

Factor $6x-2$.

$$22-\frac{-14}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $22$ times $\frac{2\left(3x-1\right)}{2\left(3x-1\right)}$.

$$\frac{22\times 2\left(3x-1\right)}{2\left(3x-1\right)}-\frac{-14}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Since $\frac{22\times 2\left(3x-1\right)}{2\left(3x-1\right)}$ and $\frac{-14}{2\left(3x-1\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{22\times 2\left(3x-1\right)-\left(-14\right)}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Do the multiplications in $22\times 2\left(3x-1\right)-\left(-14\right)$.

$$\frac{132x-44+14}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Combine like terms in $132x-44+14$.

$$\frac{132x-30}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Factor the expressions that are not already factored in $\frac{132x-30}{2\left(3x-1\right)}$.

$$\frac{6\left(22x-5\right)}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{3\left(22x-5\right)}{3x-1}-\frac{\left(16x-18\right)\times 8}{147}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3x-1$ and $147$ is $147\left(3x-1\right)$. Multiply $\frac{3\left(22x-5\right)}{3x-1}$ times $\frac{147}{147}$. Multiply $\frac{\left(16x-18\right)\times 8}{147}$ times $\frac{3x-1}{3x-1}$.

$$\frac{147\times 3\left(22x-5\right)}{147\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8\left(3x-1\right)}{147\left(3x-1\right)}$$

Since $\frac{147\times 3\left(22x-5\right)}{147\left(3x-1\right)}$ and $\frac{\left(16x-18\right)\times 8\left(3x-1\right)}{147\left(3x-1\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{147\times 3\left(22x-5\right)-\left(16x-18\right)\times 8\left(3x-1\right)}{147\left(3x-1\right)}$$

Do the multiplications in $147\times 3\left(22x-5\right)-\left(16x-18\right)\times 8\left(3x-1\right)$.

$$\frac{9702x-2205-384x^{2}+128x+432x-144}{147\left(3x-1\right)}$$

Combine like terms in $9702x-2205-384x^{2}+128x+432x-144$.

$$\frac{10262x-2349-384x^{2}}{147\left(3x-1\right)}$$

Factor the expressions that are not already factored in $\frac{10262x-2349-384x^{2}}{147\left(3x-1\right)}$.

$$\frac{-384\left(x-\left(-\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{147\left(3x-1\right)}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{-128\left(x-\left(-\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{49\left(3x-1\right)}$$

Expand $49\left(3x-1\right)$.

$$\frac{-128\left(x-\left(-\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{147x-49}$$

To find the opposite of $-\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}$, find the opposite of each term.

$$\frac{-128\left(x-\left(-\frac{1}{384}\sqrt{25425145}\right)-\frac{5131}{384}\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{147x-49}$$

The opposite of $-\frac{1}{384}\sqrt{25425145}$ is $\frac{1}{384}\sqrt{25425145}$.

$$\frac{-128\left(x+\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{147x-49}$$

To find the opposite of $\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}$, find the opposite of each term.

$$\frac{-128\left(x+\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Use the distributive property to multiply $-128$ by $x+\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}$.

$$\frac{\left(-128x-128\times \frac{1}{384}\sqrt{25425145}-128\left(-\frac{5131}{384}\right)\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-128$ and $\frac{1}{384}$ to get $\frac{-128}{384}$.

$$\frac{\left(-128x+\frac{-128}{384}\sqrt{25425145}-128\left(-\frac{5131}{384}\right)\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Reduce the fraction $\frac{-128}{384}$ to lowest terms by extracting and canceling out $128$.

$$\frac{\left(-128x-\frac{1}{3}\sqrt{25425145}-128\left(-\frac{5131}{384}\right)\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Express $-128\left(-\frac{5131}{384}\right)$ as a single fraction.

$$\frac{\left(-128x-\frac{1}{3}\sqrt{25425145}+\frac{-128\left(-5131\right)}{384}\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-128$ and $-5131$ to get $656768$.

$$\frac{\left(-128x-\frac{1}{3}\sqrt{25425145}+\frac{656768}{384}\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Reduce the fraction $\frac{656768}{384}$ to lowest terms by extracting and canceling out $128$.

$$\frac{\left(-128x-\frac{1}{3}\sqrt{25425145}+\frac{5131}{3}\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Apply the distributive property by multiplying each term of $-128x-\frac{1}{3}\sqrt{25425145}+\frac{5131}{3}$ by each term of $x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}$.

$$\frac{-128x^{2}-128x\left(-\frac{1}{384}\right)\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\sqrt{25425145}\left(-\frac{1}{384}\right)\sqrt{25425145}-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $\sqrt{25425145}$ and $\sqrt{25425145}$ to get $25425145$.

$$\frac{-128x^{2}-128x\left(-\frac{1}{384}\right)\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Express $-128\left(-\frac{1}{384}\right)$ as a single fraction.

$$\frac{-128x^{2}+\frac{-128\left(-1\right)}{384}x\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-128$ and $-1$ to get $128$.

$$\frac{-128x^{2}+\frac{128}{384}x\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Reduce the fraction $\frac{128}{384}$ to lowest terms by extracting and canceling out $128$.

$$\frac{-128x^{2}+\frac{1}{3}x\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Express $-128\left(-\frac{5131}{384}\right)$ as a single fraction.

$$\frac{-128x^{2}+\frac{1}{3}x\sqrt{25425145}+\frac{-128\left(-5131\right)}{384}x-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-128$ and $-5131$ to get $656768$.

$$\frac{-128x^{2}+\frac{1}{3}x\sqrt{25425145}+\frac{656768}{384}x-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Reduce the fraction $\frac{656768}{384}$ to lowest terms by extracting and canceling out $128$.

$$\frac{-128x^{2}+\frac{1}{3}x\sqrt{25425145}+\frac{5131}{3}x-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Combine $\frac{1}{3}x\sqrt{25425145}$ and $-\frac{1}{3}\sqrt{25425145}x$ to get $0$.

$$\frac{-128x^{2}+\frac{5131}{3}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Express $-\frac{1}{3}\times 25425145$ as a single fraction.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{-25425145}{3}\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Fraction $\frac{-25425145}{3}$ can be rewritten as $-\frac{25425145}{3}$ by extracting the negative sign.

$$\frac{-128x^{2}+\frac{5131}{3}x-\frac{25425145}{3}\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-\frac{25425145}{3}$ times $-\frac{1}{384}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{-25425145\left(-1\right)}{3\times 384}-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Do the multiplications in the fraction $\frac{-25425145\left(-1\right)}{3\times 384}$.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{25425145}{1152}-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-\frac{1}{3}$ times $-\frac{5131}{384}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{25425145}{1152}+\frac{-\left(-5131\right)}{3\times 384}\sqrt{25425145}+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Do the multiplications in the fraction $\frac{-\left(-5131\right)}{3\times 384}$.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Combine $\frac{5131}{3}x$ and $\frac{5131}{3}x$ to get $\frac{10262}{3}x$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $\frac{5131}{3}$ times $-\frac{1}{384}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}+\frac{5131\left(-1\right)}{3\times 384}\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Do the multiplications in the fraction $\frac{5131\left(-1\right)}{3\times 384}$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}+\frac{-5131}{1152}\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Fraction $\frac{-5131}{1152}$ can be rewritten as $-\frac{5131}{1152}$ by extracting the negative sign.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}-\frac{5131}{1152}\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Combine $\frac{5131}{1152}\sqrt{25425145}$ and $-\frac{5131}{1152}\sqrt{25425145}$ to get $0$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $\frac{5131}{3}$ times $-\frac{5131}{384}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131\left(-5131\right)}{3\times 384}}{147x-49}$$

Do the multiplications in the fraction $\frac{5131\left(-5131\right)}{3\times 384}$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{-26327161}{1152}}{147x-49}$$

Fraction $\frac{-26327161}{1152}$ can be rewritten as $-\frac{26327161}{1152}$ by extracting the negative sign.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}-\frac{26327161}{1152}}{147x-49}$$

Since $\frac{25425145}{1152}$ and $\frac{26327161}{1152}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145-26327161}{1152}}{147x-49}$$

Subtract $26327161$ from $25425145$ to get $-902016$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{-902016}{1152}}{147x-49}$$

Divide $-902016$ by $1152$ to get $-783$.

$$\frac{-128x^{2}+\frac{10262}{3}x-783}{147x-49}$$

Expand

$-\frac{384x^{2}-10262x+2349}{147\left(3x-1\right)}$

Short Solution Steps

Calculate $4$ to the power of $2$ and get $16$.

$$22-\frac{-14}{6x-2}-\frac{16x-6-12}{\frac{7^{2}}{8}\times 3}$$

Subtract $12$ from $-6$ to get $-18$.

$$22-\frac{-14}{6x-2}-\frac{16x-18}{\frac{7^{2}}{8}\times 3}$$

Calculate $7$ to the power of $2$ and get $49$.

$$22-\frac{-14}{6x-2}-\frac{16x-18}{\frac{49}{8}\times 3}$$

Express $\frac{49}{8}\times 3$ as a single fraction.

$$22-\frac{-14}{6x-2}-\frac{16x-18}{\frac{49\times 3}{8}}$$

Multiply $49$ and $3$ to get $147$.

$$22-\frac{-14}{6x-2}-\frac{16x-18}{\frac{147}{8}}$$

Divide $16x-18$ by $\frac{147}{8}$ by multiplying $16x-18$ by the reciprocal of $\frac{147}{8}$.

$$22-\frac{-14}{6x-2}-\frac{\left(16x-18\right)\times 8}{147}$$

Factor $6x-2$.

$$22-\frac{-14}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $22$ times $\frac{2\left(3x-1\right)}{2\left(3x-1\right)}$.

$$\frac{22\times 2\left(3x-1\right)}{2\left(3x-1\right)}-\frac{-14}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Since $\frac{22\times 2\left(3x-1\right)}{2\left(3x-1\right)}$ and $\frac{-14}{2\left(3x-1\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{22\times 2\left(3x-1\right)-\left(-14\right)}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Do the multiplications in $22\times 2\left(3x-1\right)-\left(-14\right)$.

$$\frac{132x-44+14}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Combine like terms in $132x-44+14$.

$$\frac{132x-30}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Factor the expressions that are not already factored in $\frac{132x-30}{2\left(3x-1\right)}$.

$$\frac{6\left(22x-5\right)}{2\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8}{147}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{3\left(22x-5\right)}{3x-1}-\frac{\left(16x-18\right)\times 8}{147}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3x-1$ and $147$ is $147\left(3x-1\right)$. Multiply $\frac{3\left(22x-5\right)}{3x-1}$ times $\frac{147}{147}$. Multiply $\frac{\left(16x-18\right)\times 8}{147}$ times $\frac{3x-1}{3x-1}$.

$$\frac{147\times 3\left(22x-5\right)}{147\left(3x-1\right)}-\frac{\left(16x-18\right)\times 8\left(3x-1\right)}{147\left(3x-1\right)}$$

Since $\frac{147\times 3\left(22x-5\right)}{147\left(3x-1\right)}$ and $\frac{\left(16x-18\right)\times 8\left(3x-1\right)}{147\left(3x-1\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{147\times 3\left(22x-5\right)-\left(16x-18\right)\times 8\left(3x-1\right)}{147\left(3x-1\right)}$$

Do the multiplications in $147\times 3\left(22x-5\right)-\left(16x-18\right)\times 8\left(3x-1\right)$.

$$\frac{9702x-2205-384x^{2}+128x+432x-144}{147\left(3x-1\right)}$$

Combine like terms in $9702x-2205-384x^{2}+128x+432x-144$.

$$\frac{10262x-2349-384x^{2}}{147\left(3x-1\right)}$$

Factor the expressions that are not already factored in $\frac{10262x-2349-384x^{2}}{147\left(3x-1\right)}$.

$$\frac{-384\left(x-\left(-\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{147\left(3x-1\right)}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{-128\left(x-\left(-\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{49\left(3x-1\right)}$$

Expand $49\left(3x-1\right)$.

$$\frac{-128\left(x-\left(-\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{147x-49}$$

To find the opposite of $-\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}$, find the opposite of each term.

$$\frac{-128\left(x-\left(-\frac{1}{384}\sqrt{25425145}\right)-\frac{5131}{384}\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{147x-49}$$

The opposite of $-\frac{1}{384}\sqrt{25425145}$ is $\frac{1}{384}\sqrt{25425145}$.

$$\frac{-128\left(x+\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)\left(x-\left(\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}\right)\right)}{147x-49}$$

To find the opposite of $\frac{1}{384}\sqrt{25425145}+\frac{5131}{384}$, find the opposite of each term.

$$\frac{-128\left(x+\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Use the distributive property to multiply $-128$ by $x+\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}$.

$$\frac{\left(-128x-128\times \frac{1}{384}\sqrt{25425145}-128\left(-\frac{5131}{384}\right)\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-128$ and $\frac{1}{384}$ to get $\frac{-128}{384}$.

$$\frac{\left(-128x+\frac{-128}{384}\sqrt{25425145}-128\left(-\frac{5131}{384}\right)\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Reduce the fraction $\frac{-128}{384}$ to lowest terms by extracting and canceling out $128$.

$$\frac{\left(-128x-\frac{1}{3}\sqrt{25425145}-128\left(-\frac{5131}{384}\right)\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Express $-128\left(-\frac{5131}{384}\right)$ as a single fraction.

$$\frac{\left(-128x-\frac{1}{3}\sqrt{25425145}+\frac{-128\left(-5131\right)}{384}\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-128$ and $-5131$ to get $656768$.

$$\frac{\left(-128x-\frac{1}{3}\sqrt{25425145}+\frac{656768}{384}\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Reduce the fraction $\frac{656768}{384}$ to lowest terms by extracting and canceling out $128$.

$$\frac{\left(-128x-\frac{1}{3}\sqrt{25425145}+\frac{5131}{3}\right)\left(x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}\right)}{147x-49}$$

Apply the distributive property by multiplying each term of $-128x-\frac{1}{3}\sqrt{25425145}+\frac{5131}{3}$ by each term of $x-\frac{1}{384}\sqrt{25425145}-\frac{5131}{384}$.

$$\frac{-128x^{2}-128x\left(-\frac{1}{384}\right)\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\sqrt{25425145}\left(-\frac{1}{384}\right)\sqrt{25425145}-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $\sqrt{25425145}$ and $\sqrt{25425145}$ to get $25425145$.

$$\frac{-128x^{2}-128x\left(-\frac{1}{384}\right)\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Express $-128\left(-\frac{1}{384}\right)$ as a single fraction.

$$\frac{-128x^{2}+\frac{-128\left(-1\right)}{384}x\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-128$ and $-1$ to get $128$.

$$\frac{-128x^{2}+\frac{128}{384}x\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Reduce the fraction $\frac{128}{384}$ to lowest terms by extracting and canceling out $128$.

$$\frac{-128x^{2}+\frac{1}{3}x\sqrt{25425145}-128x\left(-\frac{5131}{384}\right)-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Express $-128\left(-\frac{5131}{384}\right)$ as a single fraction.

$$\frac{-128x^{2}+\frac{1}{3}x\sqrt{25425145}+\frac{-128\left(-5131\right)}{384}x-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-128$ and $-5131$ to get $656768$.

$$\frac{-128x^{2}+\frac{1}{3}x\sqrt{25425145}+\frac{656768}{384}x-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Reduce the fraction $\frac{656768}{384}$ to lowest terms by extracting and canceling out $128$.

$$\frac{-128x^{2}+\frac{1}{3}x\sqrt{25425145}+\frac{5131}{3}x-\frac{1}{3}\sqrt{25425145}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Combine $\frac{1}{3}x\sqrt{25425145}$ and $-\frac{1}{3}\sqrt{25425145}x$ to get $0$.

$$\frac{-128x^{2}+\frac{5131}{3}x-\frac{1}{3}\times 25425145\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Express $-\frac{1}{3}\times 25425145$ as a single fraction.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{-25425145}{3}\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Fraction $\frac{-25425145}{3}$ can be rewritten as $-\frac{25425145}{3}$ by extracting the negative sign.

$$\frac{-128x^{2}+\frac{5131}{3}x-\frac{25425145}{3}\left(-\frac{1}{384}\right)-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-\frac{25425145}{3}$ times $-\frac{1}{384}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{-25425145\left(-1\right)}{3\times 384}-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Do the multiplications in the fraction $\frac{-25425145\left(-1\right)}{3\times 384}$.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{25425145}{1152}-\frac{1}{3}\sqrt{25425145}\left(-\frac{5131}{384}\right)+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $-\frac{1}{3}$ times $-\frac{5131}{384}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{25425145}{1152}+\frac{-\left(-5131\right)}{3\times 384}\sqrt{25425145}+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Do the multiplications in the fraction $\frac{-\left(-5131\right)}{3\times 384}$.

$$\frac{-128x^{2}+\frac{5131}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}+\frac{5131}{3}x+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Combine $\frac{5131}{3}x$ and $\frac{5131}{3}x$ to get $\frac{10262}{3}x$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}+\frac{5131}{3}\left(-\frac{1}{384}\right)\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $\frac{5131}{3}$ times $-\frac{1}{384}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}+\frac{5131\left(-1\right)}{3\times 384}\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Do the multiplications in the fraction $\frac{5131\left(-1\right)}{3\times 384}$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}+\frac{-5131}{1152}\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Fraction $\frac{-5131}{1152}$ can be rewritten as $-\frac{5131}{1152}$ by extracting the negative sign.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{1152}\sqrt{25425145}-\frac{5131}{1152}\sqrt{25425145}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Combine $\frac{5131}{1152}\sqrt{25425145}$ and $-\frac{5131}{1152}\sqrt{25425145}$ to get $0$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131}{3}\left(-\frac{5131}{384}\right)}{147x-49}$$

Multiply $\frac{5131}{3}$ times $-\frac{5131}{384}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{5131\left(-5131\right)}{3\times 384}}{147x-49}$$

Do the multiplications in the fraction $\frac{5131\left(-5131\right)}{3\times 384}$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}+\frac{-26327161}{1152}}{147x-49}$$

Fraction $\frac{-26327161}{1152}$ can be rewritten as $-\frac{26327161}{1152}$ by extracting the negative sign.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145}{1152}-\frac{26327161}{1152}}{147x-49}$$

Since $\frac{25425145}{1152}$ and $\frac{26327161}{1152}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{25425145-26327161}{1152}}{147x-49}$$

Subtract $26327161$ from $25425145$ to get $-902016$.

$$\frac{-128x^{2}+\frac{10262}{3}x+\frac{-902016}{1152}}{147x-49}$$

Divide $-902016$ by $1152$ to get $-783$.

$$\frac{-128x^{2}+\frac{10262}{3}x-783}{147x-49}$$