Solve (5x)/(3(x)^(2)-1)-(6(x)^(2)-2)/(3(x)^(2)-1)+((x)^(2)+x-2)/(3(x)^(2)-1) | 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

$$\frac{ 5x }{ 3 { x }^{ 2 } -1 } - \frac{ 6 { x }^{ 2 } -2 }{ 3 { x }^{ 2 } -1 } + \frac{ { x }^{ 2 } +x-2 }{ 3 { x }^{ 2 } -1 }$$

Evaluate

$\frac{x\left(6-5x\right)}{3x^{2}-1}$

Short Solution Steps

Factor the expressions that are not already factored in $\frac{6x^{2}-2}{3x^{2}-1}$.

$$\frac{5x}{3x^{2}-1}-\frac{2\left(3x^{2}-1\right)}{3x^{2}-1}+\frac{x^{2}+x-2}{3x^{2}-1}$$

Cancel out $3x^{2}-1$ in both numerator and denominator.

$$\frac{5x}{3x^{2}-1}-2+\frac{x^{2}+x-2}{3x^{2}-1}$$

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

$$\frac{5x}{3x^{2}-1}-\frac{2\left(3x^{2}-1\right)}{3x^{2}-1}+\frac{x^{2}+x-2}{3x^{2}-1}$$

Since $\frac{5x}{3x^{2}-1}$ and $\frac{2\left(3x^{2}-1\right)}{3x^{2}-1}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-2\left(3x^{2}-1\right)}{3x^{2}-1}+\frac{x^{2}+x-2}{3x^{2}-1}$$

Do the multiplications in $5x-2\left(3x^{2}-1\right)$.

$$\frac{5x-6x^{2}+2}{3x^{2}-1}+\frac{x^{2}+x-2}{3x^{2}-1}$$

Since $\frac{5x-6x^{2}+2}{3x^{2}-1}$ and $\frac{x^{2}+x-2}{3x^{2}-1}$ have the same denominator, add them by adding their numerators.

$$\frac{5x-6x^{2}+2+x^{2}+x-2}{3x^{2}-1}$$

Combine like terms in $5x-6x^{2}+2+x^{2}+x-2$.

$$\frac{6x-5x^{2}}{3x^{2}-1}$$

Expand

$\frac{6x-5x^{2}}{3x^{2}-1}$

Short Solution Steps

Factor the expressions that are not already factored in $\frac{6x^{2}-2}{3x^{2}-1}$.

$$\frac{5x}{3x^{2}-1}-\frac{2\left(3x^{2}-1\right)}{3x^{2}-1}+\frac{x^{2}+x-2}{3x^{2}-1}$$

Cancel out $3x^{2}-1$ in both numerator and denominator.

$$\frac{5x}{3x^{2}-1}-2+\frac{x^{2}+x-2}{3x^{2}-1}$$

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

$$\frac{5x}{3x^{2}-1}-\frac{2\left(3x^{2}-1\right)}{3x^{2}-1}+\frac{x^{2}+x-2}{3x^{2}-1}$$

Since $\frac{5x}{3x^{2}-1}$ and $\frac{2\left(3x^{2}-1\right)}{3x^{2}-1}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x-2\left(3x^{2}-1\right)}{3x^{2}-1}+\frac{x^{2}+x-2}{3x^{2}-1}$$

Do the multiplications in $5x-2\left(3x^{2}-1\right)$.

$$\frac{5x-6x^{2}+2}{3x^{2}-1}+\frac{x^{2}+x-2}{3x^{2}-1}$$

Since $\frac{5x-6x^{2}+2}{3x^{2}-1}$ and $\frac{x^{2}+x-2}{3x^{2}-1}$ have the same denominator, add them by adding their numerators.

$$\frac{5x-6x^{2}+2+x^{2}+x-2}{3x^{2}-1}$$

Combine like terms in $5x-6x^{2}+2+x^{2}+x-2$.

$$\frac{6x-5x^{2}}{3x^{2}-1}$$