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