( $\frac{4}{2+\sqrt[]{y} }$ + $\frac{8\sqrt[]{y} }{4-y}$ ) : ( $\frac{\sqrt[]{y}-1 }{y-2 \sqrt[]{y} }$ - $\frac{2}{\sqrt[]{y} }$ ) Rút gọn hộ mik

Đáp án+Giải thích các bước giải:

`(\frac{4}{2+\sqrt{y}}+\frac{8\sqrt{y}}{4-y} ):(\frac{\sqrt{y}-1}{y-2\sqrt{y}}-\frac{2}{\sqrt{y}})`
ĐKXĐ: `y>0;yne4`
`=(\frac{4}{2+\sqrt{y}}+\frac{8\sqrt{y}}{(2+\sqrt{y})(2-\sqrt{y})} ):(\frac{\sqrt{y}-1}{\sqrt{y}(\sqrt{y}-2)}-\frac{2}{\sqrt{y}})`

`=\frac{4(2-\sqrt{y})+8\sqrt{y}}{(2+\sqrt{y})(2-\sqrt{y})}:\frac{\sqrt{y}-1-2(\sqrt{y}-2)}{\sqrt{y}(\sqrt{y}-2)}`

`=\frac{8-4\sqrt{y}+8\sqrt{y}}{(2+\sqrt{y})(2-\sqrt{y})}:\frac{\sqrt{y}-1-2\sqrt{y}+4}{\sqrt{y}(\sqrt{y}-2)}`

`=\frac{8+4\sqrt{y}}{(2+\sqrt{y})(2-\sqrt{y})}:\frac{3-\sqrt{y}}{\sqrt{y}(\sqrt{y}-2)}`

`=\frac{4(2+\sqrt{y})}{(2+\sqrt{y})(2-\sqrt{y})}:\frac{3-\sqrt{y}}{\sqrt{y}(\sqrt{y}-2)}`

`=\frac{4}{2-\sqrt{y}}.\frac{\sqrt{y}(\sqrt{y}-2)}{3-\sqrt{y} }`

`=\frac{-4\sqrt{y}}{3-\sqrt{y} }`