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解:原式= $\frac{\sqrt{5}}{5}$
$解:原式=\sqrt {\frac {5}{2}}$
= $\frac{\sqrt{10}}{2}$
解:原式=$\frac{\sqrt{2x}}{2}$
解:原式= $\frac{3\sqrt{mn}}{n}$
$解:原式=\frac {7\sqrt {12x}}{3\sqrt {y}}$
= $\frac{14\sqrt{3xy}}{3y}$
$ 解:原式=x\sqrt {xy}×\frac {1}{\sqrt {xy}}×\sqrt {\frac {y}{x}}$
=$\sqrt{xy}$
$\frac{\sqrt{3}}{3}$
$\frac{\sqrt{6}}{2}$
$\sqrt{6}$
$\frac{\sqrt{6}}{6}$
$\frac {\sqrt {2}}{2}$
$\frac{\sqrt {6}}{3}$
解：
(1)
$\frac{2}{\sqrt{7}-\sqrt{5}}=\frac{2(\sqrt{7}+\sqrt{5})}{(\sqrt{7}-\sqrt{5})(\sqrt{7}+\sqrt{5})}=\frac{2(\sqrt{7}+\sqrt{5})}{7-5}=\sqrt{7}+\sqrt{5}$
(2)
$\frac{1}{\sqrt{3}+1}+\frac{1}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{7}+\sqrt{5}}+\dots+\frac{1}{\sqrt{2n+1}+\sqrt{2n-1}}$
$=\frac{\sqrt{3}-1}{(\sqrt{3}+1)(\sqrt{3}-1)}+\frac{\sqrt{5}-\sqrt{3}}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}+\dots+\frac{\sqrt{2n+1}-\sqrt{2n-1}}{(\sqrt{2n+1}+\sqrt{2n-1})(\sqrt{2n+1}-\sqrt{2n-1})}$
$=\frac{\sqrt{3}-1}{2}+\frac{\sqrt{5}-\sqrt{3}}{2}+\dots+\frac{\sqrt{2n+1}-\sqrt{2n-1}}{2}$
$=\frac{(\sqrt{3}-1)+(\sqrt{5}-\sqrt{3})+\dots+(\sqrt{2n+1}-\sqrt{2n-1})}{2}$
$=\frac{\sqrt{2n+1}-1}{2}$
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