Rút gọn biểu thức
a)\(\sqrt{3}-\sqrt{2}-\sqrt{\sqrt{3}+\sqrt{2}}\)
b)\(\sqrt{11-4\sqrt{7}}-\sqrt{2}\cdot\sqrt{8+3\sqrt{7}}\)
c)\(\frac{x+\sqrt{xy}}{y+\sqrt{xy}}\)
d)\(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{2\sqrt{x}-1}{x-\sqrt{x}}\left(x>0;x\ne1\right)\)
e)\(\frac{4-4\sqrt{x}}{x-2\sqrt{x}-35}+\frac{2}{\sqrt{x}-7}-\frac{3}{\sqrt{x}+5}\left(x\ge0:x\ne49\right)\)
f)\(\frac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}:\frac{1}{\sqrt{x}-\sqrt{y}}\)
f)\(\frac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}:\frac{1}{\sqrt{x}-\sqrt{y}}\)
\(=\frac{\sqrt{xy}\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{xy}}.\left(\sqrt{x}-\sqrt{y}\right)\)
\(=x-y\)
b)\(\sqrt{11-4\sqrt{7}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)
\(=\sqrt{7-4\sqrt{7}+4}-\sqrt{16+6\sqrt{7}}\)
\(=\sqrt{\left(\sqrt{7}-2\right)^2}-\sqrt{9+6\sqrt{7}+7}\)
\(=\sqrt{7}-2-\sqrt{\left(3+\sqrt{7}\right)^2}\)(vì \(\sqrt{7}>2\))
\(=\sqrt{7}-2-3-\sqrt{7}=-5\)
c)\(\frac{x+\sqrt{xy}}{y+\sqrt{xy}}=\frac{\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)}=\frac{\sqrt{x}}{\sqrt{y}}=\frac{\sqrt{xy}}{y}\)
d)\(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{2\sqrt{x}-1}{x-\sqrt{x}}=\frac{x-2\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{\sqrt{x}-1}{\sqrt{x}}=\frac{x-\sqrt{x}}{x}\)
e)\(\frac{4-4\sqrt{x}}{x-2\sqrt{x}-35}+\frac{2}{\sqrt{x}-7}-\frac{3}{\sqrt{x}+5}\)
\(=\frac{4-4\sqrt{x}}{\left(\sqrt{x}-7\right)\left(\sqrt{x}+5\right)}+\frac{2\left(\sqrt{x}+5\right)}{\left(\sqrt{x}-7\right)\left(\sqrt{x}+5\right)}-\frac{3\left(\sqrt{x}-7\right)}{\left(\sqrt{x}-7\right)\left(\sqrt{x}+5\right)}\)
\(=\frac{4-4\sqrt{x}+2\sqrt{x}+10-3\sqrt{x}+21}{\left(\sqrt{x}-7\right)\left(\sqrt{x}+5\right)}\)
\(=\frac{35-5\sqrt{x}}{\left(\sqrt{x}-7\right)\left(\sqrt{x}+5\right)}\)
\(=\frac{-5\left(\sqrt{x}-7\right)}{\left(\sqrt{x}-7\right)\left(\sqrt{x}+5\right)}\)
\(=\frac{-5}{\sqrt{x}+5}\)
c) \(\frac{x+\sqrt{xy}}{y+\sqrt{xy}}\)=\(\frac{\sqrt{x}\cdot\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{y}\cdot\left(\sqrt{x}+\sqrt{y}\right)}\)=\(\frac{\sqrt{x}}{\sqrt{y}}\)
