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