Question

Answer 1

\(P=\left(\dfrac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}+\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)^2}\right)\)

\(=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right).\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}+1}\)

\(=\dfrac{\sqrt{x}-1}{\sqrt{x}}\)

Answer 2

`(1/(x-sqrtx)+1/(sqrtx-1)):(sqrtx+1)/(x-2sqrtx+1)`
`= (1+sqrtx)/(sqrtx(sqrtx-1)):(sqrtx+1)/((sqrtx-1)^2)`
`= (1+sqrtx)/(sqrtx(sqrtx-1)).((sqrtx-1)^2)/(sqrtx+1)`
`= (sqrtx-1)/sqrtx`