Answer
$\displaystyle \frac{2x-4}{x^{2}-25}$
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.
$\displaystyle \frac{x-2}{x^{2}-25}-\frac{x-2}{25-x^{2}} \cdot \displaystyle \frac{-1}{-1}=\frac{x-2}{x^{2}-25}-\frac{-(x-2)}{-(25-x^{2})}$
$=\displaystyle \frac{x-2}{x^{2}-25}-\frac{-(x-2)}{x^{2}-25} \qquad ... -\displaystyle \frac{-A}{B}=+\frac{A}{B}$
$=\displaystyle \frac{x-2}{x^{2}-25}+\frac{(x-2)}{x^{2}-25}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
$=\displaystyle \frac{x-2+x-2}{x^{2}-25}$
= $\displaystyle \frac{2x-4}{x^{2}-25}$
