#### Answer

$\displaystyle \frac{4}{x-5}$

#### Work Step by Step

.... When one denominator is the opposite, or additive inverse of the other,
first multiply either rational expression by $\displaystyle \frac{-1}{-1}$
to obtain a common denominator.
$\displaystyle \frac{6}{x-5}+\frac{2}{5-x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{6}{x-5}+\frac{-2}{x-5}$
$= \displaystyle \frac{6}{x-5}-\frac{2}{x-5}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and
place the sum/difference over the common denominator.
If possible, factor and simplify the result.
$= \displaystyle \frac{6-2}{x-5}$
$= \displaystyle \frac{4}{x-5}$