Answer
$\displaystyle \frac{2x-16}{x^{2}-16}$
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.
$\displaystyle \frac{x-8}{x^{2}-16}-\frac{x-8}{16-x^{2}} \cdot \displaystyle \frac{-1}{-1}= \displaystyle \frac{x-8}{x^{2}-16}-\frac{-(x-8)}{-(16-x^{2})}$
$= \displaystyle \frac{x-8}{x^{2}-16}-\frac{-(x-8)}{x^{2}-16} \qquad ... -\displaystyle \frac{-A}{B}=+\frac{A}{B}$
$= \displaystyle \frac{x-8}{x^{2}-16}+\frac{(x-8)}{x^{2}-16}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
= $\displaystyle \frac{2x-16}{x^{2}-16}$
