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

May 7, 2015

Multiply both sides of the equation by the product of the two denominators:

$\frac{7}{x + 2} = \frac{2}{x - 5}$

becomes
$\frac{7}{\cancel{x + 2}} \cdot \cancel{\left(x + 2\right)} \cdot \left(x - 5\right) = \frac{2}{\cancel{x - 5}} \cdot \left(x + 2\right) \cdot \cancel{\left(x - 5\right)}$

$7 x - 35 = 2 x + 4$

$5 x = 39$

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