Question

giúp e vs mn ơi

rút gọn A= \(\left(x-\dfrac{\sqrt{xy^2+y\sqrt{y}}}{\sqrt{x}+\sqrt{y}}\right).\left(\dfrac{\sqrt{y}}{\sqrt{xy}+y}-\dfrac{\sqrt{x}}{\sqrt{xy}-x}+\dfrac{\sqrt{y}}{x-y}\right)\)

Answer 1

\(A=\left(x-\dfrac{\sqrt{y\left(xy+\sqrt{y}\right)}}{\sqrt{x}+\sqrt{y}}\right)\cdot\dfrac{\sqrt{y}\cdot\sqrt{x}\left(\sqrt{y}-\sqrt{x}\right)-\sqrt{xy}\left(\sqrt{y}+\sqrt{x}\right)-\sqrt{xy\cdot y}}{\sqrt{xy}\left(y-x\right)}\)

\(=\dfrac{x\sqrt{x}+x\sqrt{y}-\sqrt{y\left(xy+\sqrt{y}\right)}}{\sqrt{x}+\sqrt{y}}\cdot\dfrac{\sqrt{xy}\left(y-x\right)}{\sqrt{xy}\left(-2\sqrt{x}-\sqrt{y}\right)}\)

\(=\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(x\sqrt{x}+x\sqrt{y}-\sqrt{y\left(xy+\sqrt{y}\right)}\right)}{2\sqrt{x}+\sqrt{y}}\)