Question

A= \(\left(\dfrac{4\sqrt{y}}{2+\sqrt{y}}+\dfrac{8y}{4-y}\right)\) / \(\left(\dfrac{\sqrt{y}-1}{y-2\sqrt{y}}-\dfrac{2}{\sqrt{y}}\right)\)

rút gọn A

Answer 1

\(A=\left(\dfrac{4\sqrt{y}}{2+\sqrt{y}}+\dfrac{8y}{4-y}\right):\left(\dfrac{\sqrt{y}-1}{y-2\sqrt{y}}-\dfrac{2}{\sqrt{y}}\right)\)

\(=\dfrac{4\sqrt{y}\left(2-\sqrt{y}\right)+8y}{\left(2+\sqrt{y}\right)\left(2-\sqrt{y}\right)}:\dfrac{\sqrt{y}-1-2\left(\sqrt{y}-2\right)}{\sqrt{y}\left(\sqrt{y}-2\right)}\)

\(=\dfrac{8\sqrt{y}-4y+8y}{\left(2+\sqrt{y}\right)\left(2-\sqrt{y}\right)}\cdot\left(\dfrac{-\sqrt{y}\left(2-\sqrt{y}\right)}{-\left(\sqrt{y}-3\right)}\right)=\dfrac{4y\left(\sqrt{y}+2\right)}{\left(\sqrt{y}+2\right)\left(\sqrt{y}-3\right)}=\dfrac{4y}{\sqrt{y}-3}\)