# How do you simplify (2x) /( x + 4) - (x )/ (x-4)?

Mar 13, 2018

$\frac{{x}^{2} - 12 x}{\left(x + 4\right) \left(x - 4\right)}$

#### Explanation:

We have:

$\frac{2 x}{x + 4} - \frac{x}{x - 4}$

Take the $\text{LCM}$ of both denominators, which is $\left(x + 4\right) \left(x - 4\right)$, and so we got:

$\frac{2 x \left(x - 4\right)}{\left(x + 4\right) \left(x - 4\right)} - \frac{x \left(x + 4\right)}{\left(x + 4\right) \left(x - 4\right)}$

We know that: $\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$

So, we got:

$= \frac{2 x \left(x - 4\right) - x \left(x + 4\right)}{\left(x + 4\right) \left(x - 4\right)}$

Expand the numerator to get:

$= \frac{2 {x}^{2} - 8 x - {x}^{2} - 4 x}{\left(x + 4\right) \left(x - 4\right)}$

$= \frac{{x}^{2} - 12 x}{\left(x + 4\right) \left(x - 4\right)}$

This cannot be simplified further, and thus is the answer itself.