Solve (22 - (- 14))/(6x - 2) - (4 ^ 2 * x - 6 - 12)/(72/8 * 3) | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$\frac{22-(-14)}{6x-2}-\frac{4^{2}x-6-12}{72\div8\times3}$$

Evaluate

$\frac{2\left(234+35x-24x^{2}\right)}{27\left(3x-1\right)}$

Short Solution Steps

The opposite of $-14$ is $14$.

$$\frac{22+14}{6x-2}-\frac{4^{2}x-6-12}{\frac{72}{8}\times 3}$$

Add $22$ and $14$ to get $36$.

$$\frac{36}{6x-2}-\frac{4^{2}x-6-12}{\frac{72}{8}\times 3}$$

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

$$\frac{36}{6x-2}-\frac{16x-6-12}{\frac{72}{8}\times 3}$$

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

$$\frac{36}{6x-2}-\frac{16x-18}{\frac{72}{8}\times 3}$$

Divide $72$ by $8$ to get $9$.

$$\frac{36}{6x-2}-\frac{16x-18}{9\times 3}$$

Multiply $9$ and $3$ to get $27$.

$$\frac{36}{6x-2}-\frac{16x-18}{27}$$

Factor $6x-2$.

$$\frac{36}{2\left(3x-1\right)}-\frac{16x-18}{27}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2\left(3x-1\right)$ and $27$ is $54\left(3x-1\right)$. Multiply $\frac{36}{2\left(3x-1\right)}$ times $\frac{27}{27}$. Multiply $\frac{16x-18}{27}$ times $\frac{2\left(3x-1\right)}{2\left(3x-1\right)}$.

$$\frac{36\times 27}{54\left(3x-1\right)}-\frac{\left(16x-18\right)\times 2\left(3x-1\right)}{54\left(3x-1\right)}$$

Since $\frac{36\times 27}{54\left(3x-1\right)}$ and $\frac{\left(16x-18\right)\times 2\left(3x-1\right)}{54\left(3x-1\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{36\times 27-\left(16x-18\right)\times 2\left(3x-1\right)}{54\left(3x-1\right)}$$

Do the multiplications in $36\times 27-\left(16x-18\right)\times 2\left(3x-1\right)$.

$$\frac{972-96x^{2}+32x+108x-36}{54\left(3x-1\right)}$$

Combine like terms in $972-96x^{2}+32x+108x-36$.

$$\frac{936-96x^{2}+140x}{54\left(3x-1\right)}$$

Factor the expressions that are not already factored in $\frac{936-96x^{2}+140x}{54\left(3x-1\right)}$.

$$\frac{-4\times 24\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{54\left(3x-1\right)}$$

Cancel out $2\times 3$ in both numerator and denominator.

$$\frac{-2\times 8\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{9\left(3x-1\right)}$$

Expand $9\left(3x-1\right)$.

$$\frac{-2\times 8\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{27x-9}$$

Multiply $-2$ and $8$ to get $-16$.

$$\frac{-16\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{27x-9}$$

To find the opposite of $-\frac{1}{48}\sqrt{23689}+\frac{35}{48}$, find the opposite of each term.

$$\frac{-16\left(x-\left(-\frac{1}{48}\sqrt{23689}\right)-\frac{35}{48}\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{27x-9}$$

The opposite of $-\frac{1}{48}\sqrt{23689}$ is $\frac{1}{48}\sqrt{23689}$.

$$\frac{-16\left(x+\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{27x-9}$$

To find the opposite of $\frac{1}{48}\sqrt{23689}+\frac{35}{48}$, find the opposite of each term.

$$\frac{-16\left(x+\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Use the distributive property to multiply $-16$ by $x+\frac{1}{48}\sqrt{23689}-\frac{35}{48}$.

$$\frac{\left(-16x-16\times \frac{1}{48}\sqrt{23689}-16\left(-\frac{35}{48}\right)\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Multiply $-16$ and $\frac{1}{48}$ to get $\frac{-16}{48}$.

$$\frac{\left(-16x+\frac{-16}{48}\sqrt{23689}-16\left(-\frac{35}{48}\right)\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Reduce the fraction $\frac{-16}{48}$ to lowest terms by extracting and canceling out $16$.

$$\frac{\left(-16x-\frac{1}{3}\sqrt{23689}-16\left(-\frac{35}{48}\right)\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Express $-16\left(-\frac{35}{48}\right)$ as a single fraction.

$$\frac{\left(-16x-\frac{1}{3}\sqrt{23689}+\frac{-16\left(-35\right)}{48}\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Multiply $-16$ and $-35$ to get $560$.

$$\frac{\left(-16x-\frac{1}{3}\sqrt{23689}+\frac{560}{48}\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Reduce the fraction $\frac{560}{48}$ to lowest terms by extracting and canceling out $16$.

$$\frac{\left(-16x-\frac{1}{3}\sqrt{23689}+\frac{35}{3}\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Apply the distributive property by multiplying each term of $-16x-\frac{1}{3}\sqrt{23689}+\frac{35}{3}$ by each term of $x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}$.

$$\frac{-16x^{2}-16x\left(-\frac{1}{48}\right)\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\sqrt{23689}\left(-\frac{1}{48}\right)\sqrt{23689}-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $\sqrt{23689}$ and $\sqrt{23689}$ to get $23689$.

$$\frac{-16x^{2}-16x\left(-\frac{1}{48}\right)\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Express $-16\left(-\frac{1}{48}\right)$ as a single fraction.

$$\frac{-16x^{2}+\frac{-16\left(-1\right)}{48}x\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $-16$ and $-1$ to get $16$.

$$\frac{-16x^{2}+\frac{16}{48}x\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Reduce the fraction $\frac{16}{48}$ to lowest terms by extracting and canceling out $16$.

$$\frac{-16x^{2}+\frac{1}{3}x\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Express $-16\left(-\frac{35}{48}\right)$ as a single fraction.

$$\frac{-16x^{2}+\frac{1}{3}x\sqrt{23689}+\frac{-16\left(-35\right)}{48}x-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $-16$ and $-35$ to get $560$.

$$\frac{-16x^{2}+\frac{1}{3}x\sqrt{23689}+\frac{560}{48}x-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Reduce the fraction $\frac{560}{48}$ to lowest terms by extracting and canceling out $16$.

$$\frac{-16x^{2}+\frac{1}{3}x\sqrt{23689}+\frac{35}{3}x-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Combine $\frac{1}{3}x\sqrt{23689}$ and $-\frac{1}{3}\sqrt{23689}x$ to get $0$.

$$\frac{-16x^{2}+\frac{35}{3}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Express $-\frac{1}{3}\times 23689$ as a single fraction.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{-23689}{3}\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Fraction $\frac{-23689}{3}$ can be rewritten as $-\frac{23689}{3}$ by extracting the negative sign.

$$\frac{-16x^{2}+\frac{35}{3}x-\frac{23689}{3}\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $-\frac{23689}{3}$ times $-\frac{1}{48}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{-23689\left(-1\right)}{3\times 48}-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Do the multiplications in the fraction $\frac{-23689\left(-1\right)}{3\times 48}$.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{23689}{144}-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $-\frac{1}{3}$ times $-\frac{35}{48}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{23689}{144}+\frac{-\left(-35\right)}{3\times 48}\sqrt{23689}+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Do the multiplications in the fraction $\frac{-\left(-35\right)}{3\times 48}$.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Combine $\frac{35}{3}x$ and $\frac{35}{3}x$ to get $\frac{70}{3}x$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $\frac{35}{3}$ times $-\frac{1}{48}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}+\frac{35\left(-1\right)}{3\times 48}\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Do the multiplications in the fraction $\frac{35\left(-1\right)}{3\times 48}$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}+\frac{-35}{144}\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Fraction $\frac{-35}{144}$ can be rewritten as $-\frac{35}{144}$ by extracting the negative sign.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}-\frac{35}{144}\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Combine $\frac{35}{144}\sqrt{23689}$ and $-\frac{35}{144}\sqrt{23689}$ to get $0$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $\frac{35}{3}$ times $-\frac{35}{48}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35\left(-35\right)}{3\times 48}}{27x-9}$$

Do the multiplications in the fraction $\frac{35\left(-35\right)}{3\times 48}$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{-1225}{144}}{27x-9}$$

Fraction $\frac{-1225}{144}$ can be rewritten as $-\frac{1225}{144}$ by extracting the negative sign.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}-\frac{1225}{144}}{27x-9}$$

Since $\frac{23689}{144}$ and $\frac{1225}{144}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689-1225}{144}}{27x-9}$$

Subtract $1225$ from $23689$ to get $22464$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{22464}{144}}{27x-9}$$

Divide $22464$ by $144$ to get $156$.

$$\frac{-16x^{2}+\frac{70}{3}x+156}{27x-9}$$

Factor the expressions that are not already factored.

$$\frac{-\frac{2}{3}\times 24\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{9\left(3x-1\right)}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{-\frac{2}{3}\times 8\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{3\left(3x-1\right)}$$

Expand the expression.

$$\frac{-\frac{16}{3}x^{2}+\frac{70}{9}x+52}{9x-3}$$

Factor the expressions that are not already factored.

$$\frac{-\frac{2}{9}\times 24\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{3\left(3x-1\right)}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{-\frac{2}{9}\times 8\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{3x-1}$$

Expand the expression.

$$\frac{-\frac{16}{9}x^{2}+\frac{70}{27}x+\frac{52}{3}}{3x-1}$$

Expand

$-\frac{2\left(24x^{2}-35x-234\right)}{27\left(3x-1\right)}$

Short Solution Steps

The opposite of $-14$ is $14$.

$$\frac{22+14}{6x-2}-\frac{4^{2}x-6-12}{\frac{72}{8}\times 3}$$

Add $22$ and $14$ to get $36$.

$$\frac{36}{6x-2}-\frac{4^{2}x-6-12}{\frac{72}{8}\times 3}$$

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

$$\frac{36}{6x-2}-\frac{16x-6-12}{\frac{72}{8}\times 3}$$

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

$$\frac{36}{6x-2}-\frac{16x-18}{\frac{72}{8}\times 3}$$

Divide $72$ by $8$ to get $9$.

$$\frac{36}{6x-2}-\frac{16x-18}{9\times 3}$$

Multiply $9$ and $3$ to get $27$.

$$\frac{36}{6x-2}-\frac{16x-18}{27}$$

Factor $6x-2$.

$$\frac{36}{2\left(3x-1\right)}-\frac{16x-18}{27}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2\left(3x-1\right)$ and $27$ is $54\left(3x-1\right)$. Multiply $\frac{36}{2\left(3x-1\right)}$ times $\frac{27}{27}$. Multiply $\frac{16x-18}{27}$ times $\frac{2\left(3x-1\right)}{2\left(3x-1\right)}$.

$$\frac{36\times 27}{54\left(3x-1\right)}-\frac{\left(16x-18\right)\times 2\left(3x-1\right)}{54\left(3x-1\right)}$$

Since $\frac{36\times 27}{54\left(3x-1\right)}$ and $\frac{\left(16x-18\right)\times 2\left(3x-1\right)}{54\left(3x-1\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{36\times 27-\left(16x-18\right)\times 2\left(3x-1\right)}{54\left(3x-1\right)}$$

Do the multiplications in $36\times 27-\left(16x-18\right)\times 2\left(3x-1\right)$.

$$\frac{972-96x^{2}+32x+108x-36}{54\left(3x-1\right)}$$

Combine like terms in $972-96x^{2}+32x+108x-36$.

$$\frac{936-96x^{2}+140x}{54\left(3x-1\right)}$$

Factor the expressions that are not already factored in $\frac{936-96x^{2}+140x}{54\left(3x-1\right)}$.

$$\frac{-4\times 24\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{54\left(3x-1\right)}$$

Cancel out $2\times 3$ in both numerator and denominator.

$$\frac{-2\times 8\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{9\left(3x-1\right)}$$

Expand $9\left(3x-1\right)$.

$$\frac{-2\times 8\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{27x-9}$$

Multiply $-2$ and $8$ to get $-16$.

$$\frac{-16\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{27x-9}$$

To find the opposite of $-\frac{1}{48}\sqrt{23689}+\frac{35}{48}$, find the opposite of each term.

$$\frac{-16\left(x-\left(-\frac{1}{48}\sqrt{23689}\right)-\frac{35}{48}\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{27x-9}$$

The opposite of $-\frac{1}{48}\sqrt{23689}$ is $\frac{1}{48}\sqrt{23689}$.

$$\frac{-16\left(x+\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{27x-9}$$

To find the opposite of $\frac{1}{48}\sqrt{23689}+\frac{35}{48}$, find the opposite of each term.

$$\frac{-16\left(x+\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Use the distributive property to multiply $-16$ by $x+\frac{1}{48}\sqrt{23689}-\frac{35}{48}$.

$$\frac{\left(-16x-16\times \frac{1}{48}\sqrt{23689}-16\left(-\frac{35}{48}\right)\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Multiply $-16$ and $\frac{1}{48}$ to get $\frac{-16}{48}$.

$$\frac{\left(-16x+\frac{-16}{48}\sqrt{23689}-16\left(-\frac{35}{48}\right)\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Reduce the fraction $\frac{-16}{48}$ to lowest terms by extracting and canceling out $16$.

$$\frac{\left(-16x-\frac{1}{3}\sqrt{23689}-16\left(-\frac{35}{48}\right)\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Express $-16\left(-\frac{35}{48}\right)$ as a single fraction.

$$\frac{\left(-16x-\frac{1}{3}\sqrt{23689}+\frac{-16\left(-35\right)}{48}\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Multiply $-16$ and $-35$ to get $560$.

$$\frac{\left(-16x-\frac{1}{3}\sqrt{23689}+\frac{560}{48}\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Reduce the fraction $\frac{560}{48}$ to lowest terms by extracting and canceling out $16$.

$$\frac{\left(-16x-\frac{1}{3}\sqrt{23689}+\frac{35}{3}\right)\left(x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}\right)}{27x-9}$$

Apply the distributive property by multiplying each term of $-16x-\frac{1}{3}\sqrt{23689}+\frac{35}{3}$ by each term of $x-\frac{1}{48}\sqrt{23689}-\frac{35}{48}$.

$$\frac{-16x^{2}-16x\left(-\frac{1}{48}\right)\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\sqrt{23689}\left(-\frac{1}{48}\right)\sqrt{23689}-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $\sqrt{23689}$ and $\sqrt{23689}$ to get $23689$.

$$\frac{-16x^{2}-16x\left(-\frac{1}{48}\right)\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Express $-16\left(-\frac{1}{48}\right)$ as a single fraction.

$$\frac{-16x^{2}+\frac{-16\left(-1\right)}{48}x\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $-16$ and $-1$ to get $16$.

$$\frac{-16x^{2}+\frac{16}{48}x\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Reduce the fraction $\frac{16}{48}$ to lowest terms by extracting and canceling out $16$.

$$\frac{-16x^{2}+\frac{1}{3}x\sqrt{23689}-16x\left(-\frac{35}{48}\right)-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Express $-16\left(-\frac{35}{48}\right)$ as a single fraction.

$$\frac{-16x^{2}+\frac{1}{3}x\sqrt{23689}+\frac{-16\left(-35\right)}{48}x-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $-16$ and $-35$ to get $560$.

$$\frac{-16x^{2}+\frac{1}{3}x\sqrt{23689}+\frac{560}{48}x-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Reduce the fraction $\frac{560}{48}$ to lowest terms by extracting and canceling out $16$.

$$\frac{-16x^{2}+\frac{1}{3}x\sqrt{23689}+\frac{35}{3}x-\frac{1}{3}\sqrt{23689}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Combine $\frac{1}{3}x\sqrt{23689}$ and $-\frac{1}{3}\sqrt{23689}x$ to get $0$.

$$\frac{-16x^{2}+\frac{35}{3}x-\frac{1}{3}\times 23689\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Express $-\frac{1}{3}\times 23689$ as a single fraction.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{-23689}{3}\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Fraction $\frac{-23689}{3}$ can be rewritten as $-\frac{23689}{3}$ by extracting the negative sign.

$$\frac{-16x^{2}+\frac{35}{3}x-\frac{23689}{3}\left(-\frac{1}{48}\right)-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $-\frac{23689}{3}$ times $-\frac{1}{48}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{-23689\left(-1\right)}{3\times 48}-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Do the multiplications in the fraction $\frac{-23689\left(-1\right)}{3\times 48}$.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{23689}{144}-\frac{1}{3}\sqrt{23689}\left(-\frac{35}{48}\right)+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $-\frac{1}{3}$ times $-\frac{35}{48}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{23689}{144}+\frac{-\left(-35\right)}{3\times 48}\sqrt{23689}+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Do the multiplications in the fraction $\frac{-\left(-35\right)}{3\times 48}$.

$$\frac{-16x^{2}+\frac{35}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}+\frac{35}{3}x+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Combine $\frac{35}{3}x$ and $\frac{35}{3}x$ to get $\frac{70}{3}x$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}+\frac{35}{3}\left(-\frac{1}{48}\right)\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $\frac{35}{3}$ times $-\frac{1}{48}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}+\frac{35\left(-1\right)}{3\times 48}\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Do the multiplications in the fraction $\frac{35\left(-1\right)}{3\times 48}$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}+\frac{-35}{144}\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Fraction $\frac{-35}{144}$ can be rewritten as $-\frac{35}{144}$ by extracting the negative sign.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{144}\sqrt{23689}-\frac{35}{144}\sqrt{23689}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Combine $\frac{35}{144}\sqrt{23689}$ and $-\frac{35}{144}\sqrt{23689}$ to get $0$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35}{3}\left(-\frac{35}{48}\right)}{27x-9}$$

Multiply $\frac{35}{3}$ times $-\frac{35}{48}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{35\left(-35\right)}{3\times 48}}{27x-9}$$

Do the multiplications in the fraction $\frac{35\left(-35\right)}{3\times 48}$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}+\frac{-1225}{144}}{27x-9}$$

Fraction $\frac{-1225}{144}$ can be rewritten as $-\frac{1225}{144}$ by extracting the negative sign.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689}{144}-\frac{1225}{144}}{27x-9}$$

Since $\frac{23689}{144}$ and $\frac{1225}{144}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{23689-1225}{144}}{27x-9}$$

Subtract $1225$ from $23689$ to get $22464$.

$$\frac{-16x^{2}+\frac{70}{3}x+\frac{22464}{144}}{27x-9}$$

Divide $22464$ by $144$ to get $156$.

$$\frac{-16x^{2}+\frac{70}{3}x+156}{27x-9}$$

Factor the expressions that are not already factored.

$$\frac{-\frac{2}{3}\times 24\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{9\left(3x-1\right)}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{-\frac{2}{3}\times 8\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{3\left(3x-1\right)}$$

Expand the expression.

$$\frac{-\frac{16}{3}x^{2}+\frac{70}{9}x+52}{9x-3}$$

Factor the expressions that are not already factored.

$$\frac{-\frac{2}{9}\times 24\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{3\left(3x-1\right)}$$

Cancel out $3$ in both numerator and denominator.

$$\frac{-\frac{2}{9}\times 8\left(x-\left(-\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)\left(x-\left(\frac{1}{48}\sqrt{23689}+\frac{35}{48}\right)\right)}{3x-1}$$

Expand the expression.

$$\frac{-\frac{16}{9}x^{2}+\frac{70}{27}x+\frac{52}{3}}{3x-1}$$