Answer
$\dfrac{x-y}{x-2\sqrt{xy}+y}$
Work Step by Step
Multiplying by the conjugate of the numerator, then the rationalized-numerator form of the given expression, $
\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}\cdot\dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}
\\\\=
\dfrac{(\sqrt{x})^2-(\sqrt{y})^2}{(\sqrt{x}-\sqrt{y})^2}
\\\\=
\dfrac{x-y}{(\sqrt{x})^2+2(\sqrt{x})(-\sqrt{y})+(-\sqrt{y})^2}
\\\\=
\dfrac{x-y}{x-2\sqrt{xy}+y}
.\end{array}