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