Question

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

Rút gọn

Answer 1

Với `y > 0,y \ne 1` có:

`Q=(1/[y-\sqrt{y}]+1/[\sqrt{y}-1]):[\sqrt{y}+1]/[y-2\sqrt{y}+1]`

`Q=[1+\sqrt{y}]/[\sqrt{y}(\sqrt{y}-1)].[(\sqrt{y}-1)^2]/[\sqrt{y}+1]`

`Q=[\sqrt{y}-1]/\sqrt{y}`

Answer 2

\(Q=\left(\dfrac{1}{\sqrt{y}\left(\sqrt{y}-1\right)}+\dfrac{\sqrt{y}}{\sqrt{y}-1}\right)\cdot\dfrac{\left(\sqrt{y}-1\right)^2}{\sqrt{y}+1}\)

\(=\dfrac{\sqrt{y}+1}{\sqrt{y}\left(\sqrt{y}-1\right)}\cdot\dfrac{\left(\sqrt{y}-1\right)^2}{\sqrt{y}+1}=\dfrac{\sqrt{y}-1}{\sqrt{y}}\)