Bài 11:
a: \(\frac{x\cdot\sqrt{x}-y\cdot\sqrt{y}}{\sqrt{x}-\sqrt{y}}\)
\(=\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\sqrt{x}-\sqrt{y}}\)
\(=x+\sqrt{xy}+y\)
b: \(\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt3}\)
\(=\frac{x-\sqrt{3x}+3}{\left(\sqrt{x}+\sqrt3\right)\left(x-\sqrt{3x}+3\right)}\)
\(=\frac{1}{\sqrt{x}+\sqrt3}\)
Bài 9:
a: \(\frac{\sqrt5-\sqrt3}{\sqrt2}=\frac{\sqrt2\left(\sqrt5-\sqrt3\right)}{2}=\frac{\sqrt{10}-\sqrt6}{2}\)
b: \(\frac{26}{5-2\sqrt3}=\frac{26\left(5+2\sqrt3\right)}{\left(5-2\sqrt3\right)\left(5+2\sqrt3\right)}=\frac{26\left(5+2\sqrt3\right)}{13}=2\left(5+2\sqrt3\right)=10+4\sqrt3\)
c: \(\frac{2\sqrt{10}-5}{4-\sqrt{10}}=\frac{\sqrt5\left(2\sqrt2-\sqrt5\right)}{\sqrt2\left(2\sqrt2-\sqrt5\right)}=\frac{\sqrt5}{\sqrt2}=\frac{\sqrt{10}}{2}\)
d: \(\frac{9-2\sqrt3}{3\sqrt6-2\sqrt2}=\frac{\sqrt3\left(3\sqrt3-2\right)}{\sqrt2\cdot\left(3\sqrt3-2\right)}=\frac{\sqrt3}{\sqrt2}=\frac{\sqrt6}{2}\)
