# How can you evaluate (x-2)/(x-6) - (x+2)/(6-x) ?

Jul 14, 2015

$\frac{x - 2}{x - 6} - \frac{x + 2}{6 - x} = \frac{2 x}{x - 6}$

#### Explanation:

$\frac{x + 2}{6 - x} = \frac{x + 2}{\left(- 1\right) \left(x - 6\right)} = - \frac{x + 2}{x - 6}$

So
$\frac{x - 2}{x - 6} - \frac{x + 2}{6 - x}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{x - 2}{x - 6} - \left(- 1\right) \frac{x + 2}{x - 6}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{x - 2}{x - 6} + \frac{x + 2}{x - 6}$

and since, in general $\frac{a}{d} + \frac{b}{d} = \frac{a + b}{d}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{x - 2 + x + 2}{x - 6}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{2 x}{x - 6}$