# How do you solve (x-2)/(x+5) - 4/(x+1) = 1/(x+1)?

Mar 17, 2018

$x = 9$ or $x = - 3$

#### Explanation:

First, lets rewrite the equation in the form

$\frac{x - 2}{x + 5} - \frac{5}{x + 1} = 0$

Then we multiply both sides of the equation by $\left(x + 5\right) \left(x + 1\right)$ to get rid of the denominators.

This changes the equation to

$\left(x - 2\right) \left(x + 1\right) - 5 \left(x + 5\right) = 0 \implies$
$\left({x}^{2} - x - 2\right) - \left(5 x + 25\right) = 0 \implies$
${x}^{2} - 6 x - 27 = 0 \implies$
${x}^{2} - 9 x + 3 x - 27 = 0 \implies$
$x \left(x - 9\right) + 3 \left(x - 9\right) = 0 \implies$
$\left(x - 9\right) \left(x + 3\right) = 0$

Thus, either $x = 9$ or $x = - 3$