$ĐKXĐ: x\ge0; y\ge0; x\ne y$
$\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}-\sqrt{y})^{2}$
$=\dfrac{(\sqrt{x})^{3}+(\sqrt{y})^{3}}{\sqrt{x}+\sqrt{y}}-(x-2\sqrt{xy}+y)$
$=\dfrac{(\sqrt{x}+\sqrt{y})(x-\sqrt{xy}+y)}{\sqrt{x}+\sqrt{y}}-x+2\sqrt{xy}-y$
$=x-\sqrt{xy}+y-x+2\sqrt{xy}-y$
$=\sqrt{xy}$
Vậy với $x\ge0; y\ge0; x\ne y$ thì $\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-(\sqrt{x}-\sqrt{y})^{2}=\sqrt{xy}$
