\(=\dfrac{x+y}{\sqrt{x}+\sqrt{y}}:\left(\dfrac{x+y}{\sqrt{xy}}+\dfrac{y}{\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)}-\dfrac{x}{\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)}\right)\)
\(=\dfrac{x+y}{\sqrt{x}+\sqrt{y}}:\dfrac{x^2-y^2+y\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)-x\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)}{\left(x-y\right)\cdot\sqrt{xy}}\)
\(=\dfrac{x+y}{\sqrt{x}+\sqrt{y}}\cdot\left(x-y\right)\cdot\dfrac{\sqrt{xy}}{x^2-y^2+y\sqrt{xy}+y^2-x^2+x\sqrt{xy}}\)
\(=\dfrac{x+y}{\sqrt{x}+\sqrt{y}}\cdot\left(x-y\right)\cdot\dfrac{\sqrt{xy}}{\left(\sqrt{x}+\sqrt{y}\right)\cdot\sqrt{xy}}\)
\(=\dfrac{x^2-y^2}{x+2\sqrt{xy}+y}\)
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