=\(\left(\frac{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}-\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}\right).\frac{\sqrt{x}+\sqrt{y}}{x-\sqrt{xy}+y}\)
\(=\left[\left(\sqrt{x}+\sqrt{y}\right)-\frac{x+\sqrt{xy}+y}{\sqrt{x}+\sqrt{y}}\right].\frac{\sqrt{x}+\sqrt{y}}{x-\sqrt{xy}+y}\)
\(=\frac{x+2\sqrt{xy}+y-x-\sqrt{xy}-y}{\sqrt{x}+\sqrt{y}}.\frac{\sqrt{x}+\sqrt{y}}{x-\sqrt{xy}+y}\)
\(=\frac{\sqrt{xy}}{x-\sqrt{xy}+y}\)
Mình gi rút gọn bạn tự hiểu nha:
\(\left(\frac{x-y}{\sqrt{x}-\sqrt{y}}+\frac{\sqrt{x^3}-\sqrt{y^3}}{y-x}\right):\frac{\left(\sqrt{x}-\sqrt{y}\right)^2+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\)
=\(\left(\sqrt{x}-\sqrt{y}-\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)}{x-y}\right).\frac{\sqrt{x}+\sqrt{y}}{x+y-\sqrt{xy}}\)
=\(\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{x+y-\sqrt{xy}}-\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)\left(x+y-\sqrt{xy}\right)}{\left(x-y\right)\left(x+y-\sqrt{xy}\right)}\)
=