# How do you solve 8+6/(x-5)=(x-13)/(x-5) and check for extraneous solutions?

##### 1 Answer
Sep 8, 2016

$x = 3$

#### Explanation:

Check for restrictions on $x$ first. The denominator may not be 0.
$x - 5 = 0 \rightarrow x = 5 \text{ } \rightarrow$ So $x \ne 5$

The denominators of the fractions are the same, so we can put them on the same side and add them together.

$8 = \frac{x - 13}{x - 5} - \frac{6}{x - 5}$

$8 = \frac{x - 13 - 6}{x - 5}$

$8 = \frac{x - 19}{x - 5} \text{ } \leftarrow$ now cross-multiply

$8 x - 40 = x - 19$

$8 x - x = 40 - 19$

$7 x = 21$

$x = 3$