Answer
$2\sqrt{x}+2\sqrt{y}$
Work Step by Step
We simplify the fraction by multiplying through by $\sqrt{x}+\sqrt{y}$ and using the fact that $(a-b)(a+b)=a^2-b^2$:
$\displaystyle \frac{2(x-y)}{\sqrt{x}-\sqrt{y}}=\frac{2(x-y)}{\sqrt{x}-\sqrt{y}} \displaystyle \frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}+\sqrt{y}}=\frac{2(x-y)(\sqrt{x}+\sqrt{y})}{x-y}=2(\sqrt{x}+\sqrt{y})=2\sqrt{x}+2\sqrt{y}$
