# How do you solve \frac { 8} { x } + \frac { 2} { x - 4} = \frac { x - 2} { x - 4}?

Oct 16, 2017

$x = 8$

#### Explanation:

$\frac{8}{x} + \frac{2}{x - 4} = \frac{x - 2}{x - 4}$

$\frac{8}{x} = - \frac{2}{x - 4} + \frac{x - 2}{x - 4} = \frac{- 2 + x - 2}{x - 4} = \frac{x - 4}{x - 4} = 1$

$\frac{8}{x} = 1$

$\frac{8}{\cancel{x}} \left(\cancel{x}\right) = 1 \left(x\right)$

$8 = x$

To check, change all $x$ to $8$:

$\frac{8}{8} + \frac{2}{8 - 4} = \frac{8 - 2}{8 - 4}$

$1 + \frac{1}{2} = \frac{6}{4}$

$1 \frac{1}{2} = 1 \frac{1}{2}$