Answer
$\dfrac{4\sqrt{ax}+2\sqrt{ay}}{4x-y}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{2\sqrt{a}}{2\sqrt{x}-\sqrt{y}}
$ results to
\begin{array}{l}
\dfrac{2\sqrt{a}}{2\sqrt{x}-\sqrt{y}}
\cdot
\dfrac{2\sqrt{x}+\sqrt{y}}{2\sqrt{x}+\sqrt{y}}
\\\\=
\dfrac{4\sqrt{ax}+2\sqrt{ay}}{(2\sqrt{x})^2-(\sqrt{y})^2}
\\\\=
\dfrac{4\sqrt{ax}+2\sqrt{ay}}{4x-y}
.\end{array}