Question

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

Answer 1

分析 首先將括號里面分母有理化，再通分運(yùn)算，結(jié)合二次根式除法運(yùn)算法則化簡求出即可．

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．

點(diǎn)評 此題主要考查了二次根式的混合運(yùn)算，正確分母有理化是解題關(guān)鍵．