How do you solve -3/(x+1)=4/(x-1)?

May 2, 2017

Multiply each side by the denominators and simplify.

Explanation:

$- \frac{3}{\textcolor{red}{x + 1}} = \frac{4}{\textcolor{b l u e}{x - 1}}$

First off, multiply both sides by the denominators.

$- \frac{\textcolor{b l u e}{3 \left(x - 1\right)}}{\textcolor{red}{x + 1}} = 4$

-color(blue)(3(x-1))= color(red)(4(x+1)

Then, expand the brackets.

$\textcolor{b l u e}{- 3 x + 3} = \textcolor{red}{4 x + 4}$

Rearrange the equation.

$- 3 x - 4 x = 4 - 3$

$$              x=-1/7


Double check your answer by substituting $x = - \frac{1}{7}$ back into the original equation.

$- \frac{3}{\textcolor{red}{- \frac{1}{7} + 1}} = \frac{4}{\textcolor{b l u e}{- \frac{1}{7} - 1}}$

color(red)(-3.5 = color(blue)(-3.5)

Therefore, your answer $x = - 3.5$ is correct.