# How do you solve the equation and identify any extraneous solutions for x/(x-2) - 5 = 2/(x-2)?

Jun 9, 2015

This equation has no solutions.

#### Explanation:

Starting with:

$\frac{x}{x - 2} - 5 = \frac{2}{x - 2}$

subtract $\frac{2}{x - 2}$ from both sides to get:

$0 = \frac{x}{x - 2} - \frac{2}{x - 2} - 5$

$= \frac{x - 2}{x - 2} - 5$

$= 1 - 5$

$= - 4$

with exclusion $x \ne 2$