Question

7．计算：（$\sqrt{xy}$-$\frac{xy}{x+\sqrt{xy}}$）÷$\frac{\sqrt{xy}-y}{x-y}$．

Answer 1

分析 首先将括号里面分母有理化，再通分运算，结合二次根式除法运算法则化简求出即可．

解答 解：（$\sqrt{xy}$-$\frac{xy}{x+\sqrt{xy}}$）÷$\frac{\sqrt{xy}-y}{x-y}$
=[$\sqrt{xy}$-$\frac{xy（x-\sqrt{xy}）}{（x+\sqrt{xy}）（x-\sqrt{xy}）}$]×$\frac{x-y}{\sqrt{xy}-y}$
=[$\sqrt{xy}$-$\frac{y（x-\sqrt{xy}）}{x-y}$]×$\frac{x-y}{\sqrt{xy}-y}$
=$\frac{（x-y）\sqrt{xy}-y（x-\sqrt{xy}）}{x-y}$×$\frac{x-y}{\sqrt{xy}-y}$
=$\frac{x（\sqrt{xy}-y）}{x-y}$×$\frac{x-y}{\sqrt{xy}-y}$
=x．

点评 此题主要考查了二次根式的混合运算，正确分母有理化是解题关键．