[tex]\frac{(\sqrt{x}-\sqrt{y})^2+4\sqrt{xy}}{\sqrt{x}+\sqrt{y}}-\frac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}=\frac{x-2\sqrt{xy}+y+4\sqrt{xy}}{\sqrt{x}+\sqrt{y}}-\frac{\sqrt{xy}.(\sqrt{x}+\sqrt{y})}{\sqrt{xy}}=\frac{(\sqrt{x}+\sqrt{y})^2}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}+\sqrt{y})=\sqrt{x}+\sqrt{y}-\sqrt{x}-\sqrt{y}=0[/tex]
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