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

Oct 8, 2015

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

#### Explanation:

You need to find the common denominator of the two fractions. Notice that you can multiply the first fraction by $1 = \frac{x - 2}{x - 2}$ and the second fraction by $1 = \frac{x + 2}{x + 2}$ to get

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

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

Expand the parantheses in the numerator to cancel out like terms

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{{x}^{2}}}} - 2 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{{x}^{2}}}} - 2 x}{\left(x - 2\right) \left(x + 2\right)}$

The final form of the expression will thus be

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