# How do you simplify x/(x+5)+(5x)/(x-5)?

Oct 22, 2015

Convert the terms to a common denominator then add the numerators and simplify.

$\textcolor{w h i t e}{\text{XXX}} \frac{2 x \left(3 x - 10\right)}{{x}^{2} - 25}$

#### Explanation:

$\frac{x}{x + 5} + \frac{5 x}{x - 5}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{x \left(x - 5\right)}{\left(x + 5\right) \left(x - 5\right)} + \frac{5 x \left(x + 5\right)}{\left(x + 5\right) \left(x - 5\right)}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{{x}^{2} - 5 x + 5 {x}^{2} + 25 x}{\left(x + 5\right) \left(x - 5\right)}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{6 {x}^{2} - 20 x}{\left(x + 5\right) \left(x - 5\right)}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{2 x \left(3 x - 10\right)}{{x}^{2} - 25}$