Answer
$\displaystyle \frac{16}{x-2}$
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.
$\displaystyle \frac{10}{x-2}-\frac{6}{2-x} \cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{10}{x-2}-\frac{-6}{-(2-x)}$
$= \displaystyle \frac{10}{x-2}-\frac{-6}{x-2} \qquad ... -\displaystyle \frac{-A}{B}=+\frac{A}{B}$
$= \displaystyle \frac{10}{x-2}+\frac{6}{x-2}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
$= \displaystyle \frac{10+6}{x-2}$
= $\displaystyle \frac{16}{x-2}$