Rút gọn biểu thức 

- Hướng dẫn giải

Ta có

$\begin{array}{l}B=\frac{x+y+2\sqrt{xy}}{x\sqrt{x}-y\sqrt{y}+x\sqrt{y}-y\sqrt{x}}\\ =\frac{{\left(\sqrt{x}+\sqrt{y}\right)}^2}{x\sqrt{x}-y\sqrt{y}+x\sqrt{y}-y\sqrt{x}}\\ =\frac{{\left(\sqrt{x}+\sqrt{y}\right)}^2}{x\left(\sqrt{x}+\sqrt{y}\right)-y\left(\sqrt{y}+\sqrt{x}\right)}\\ =\frac{{\left(\sqrt{x}+\sqrt{y}\right)}^2}{\left(\sqrt{x}+\sqrt{y}\right)\left(x-y\right)}\\ =\frac{\left(\sqrt{x}+\sqrt{y}\right)}{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}\\ =\frac{1}{\sqrt{x}-\sqrt{y}}\end{array}$