# How do you combine \frac { 3} { x - 6} - \frac { 3} { x + 2} into one expression?

Apr 1, 2018

$\frac{24}{\left(x - 6\right) \left(x - 2\right)}$

#### Explanation:

The denominators need to be the same to combine the fractions so times $\left(x + 2\right)$ to the Left fraction and $\left(x - 6\right)$ to the right one.

$\frac{3}{x - 6} \cdot \frac{x + 2}{x + 2} - \frac{3}{x + 2} \cdot \frac{x - 6}{x - 6}$

$\frac{3 \left(x + 2\right)}{\left(x - 6\right) \left(x - 2\right)} - \frac{3 \left(x - 6\right)}{\left(x + 2\right) \left(x - 6\right)}$

$\frac{3 \left(x + 2\right) - 3 \left(x - 6\right)}{\left(x - 6\right) \left(x - 2\right)}$

$\frac{3 x + 6 - 3 x + 18}{\left(x - 6\right) \left(x - 2\right)}$

$\frac{24}{\left(x - 6\right) \left(x - 2\right)}$