# How do you solve 7/(x+2)= 2/(x-5)?

May 2, 2016

$x = \frac{39}{5} = 7 \frac{4}{5}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX")7/(x+2)=2/(x-5)color(white)("XXX}}$note: this equation implies $x \ne - 2$ and $x \ne 5$

Multiply both sides by $\left(x + 2\right) \left(x - 5\right)$ (sometimes this will be called "cross multiplying")
$\textcolor{w h i t e}{\text{XXX}} 7 \left(x - 5\right) = 2 \left(x + 2\right)$
simplify:
$\textcolor{w h i t e}{\text{XXX}} 7 x - 35 = 2 x + 4$
subtract $2 x$ from both sides and add $35$ to both sides
$\textcolor{w h i t e}{\text{XXX}} 5 x = 39$
divide both sides by $5$
$\textcolor{w h i t e}{\text{XXX}} x = \frac{39}{5}$