[tex]P=\left ( \sqrt{x} +\frac{y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right )\div \left ( \frac{x}{\sqrt{xy}+y}+\frac{y}{\sqrt{xy}-x} -\frac{x+y}{\sqrt{xy}}\right )[/tex]
$P=\left ( \sqrt{x} +\dfrac{y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\right ): \left ( \dfrac{x}{\sqrt{xy}+y}+\dfrac{y}{\sqrt{xy}-x} -\dfrac{x+y}{\sqrt{xy}}\right )\\=\dfrac{x+\sqrt{xy}+y-\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\left [ \dfrac{x}{\sqrt{y}(\sqrt{x}+\sqrt{y})}-\dfrac{y}{\sqrt{x}(\sqrt{x}-\sqrt{y})}-\dfrac{x+y}{\sqrt{xy}} \right ]\\=\dfrac{x+y}{\sqrt{x}+\sqrt{y}}:\dfrac{x\sqrt{x}(\sqrt{x}-\sqrt{y})-y\sqrt{y}(\sqrt{x}+\sqrt{y})-(x+y)(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}{\sqrt{xy}(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}\\=\dfrac{x+y}{\sqrt{x}+\sqrt{y}}:\dfrac{x^2-x\sqrt{xy}-y\sqrt{xy}-y^2-x^2+y^2}{\sqrt{xy}(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}\\=\dfrac{x+y}{\sqrt{x}+\sqrt{y}}.\dfrac{\sqrt{xy}(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}{-\sqrt{xy}(x+y)}\\=-(\sqrt{x}-\sqrt{y})=\sqrt{y}-\sqrt{x}$
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
