`***`Lời giải`***`

a)

`P=(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}):(\frac{\sqrt{x}+1}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}-1})` 
ĐKXĐ: `x>0;xne1;xne4`
`=\frac{\sqrt{x}-(\sqrt{x}-1)}{\sqrt{x}(\sqrt{x}-1)}:\frac{(\sqrt{x}-1)(\sqrt{x}+1)-(\sqrt{x}+2)(\sqrt{x}-2)}{(\sqrt{x}-1)(\sqrt{x}-2)}`

`=\frac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}(\sqrt{x}-1)}:\frac{x-1-(x-4)}{(\sqrt{x}-1)(\sqrt{x}-2)}`
`=\frac{1}{\sqrt{x}(\sqrt{x}-1)}:\frac{3}{(\sqrt{x}-1)(\sqrt{x}-2)}`
`=\frac{1}{\sqrt{x}(\sqrt{x}-1)}.\frac{(\sqrt{x}-1)(\sqrt{x}-2)}{3}`
`=\frac{\sqrt{x}-2}{3\sqrt{x}}`
Vậy `P=\frac{\sqrt{x}-2}{3\sqrt{x}}` với `x>0;xne1;xne4`

b)

Ta có: `P=1/4`

`=>\frac{\sqrt{x}-2}{3\sqrt{x}}=1/4`

`<=>\frac{\sqrt{x}-2}{3\sqrt{x}}-1/4=0`

`<=>\frac{4(\sqrt{x}-2)-3\sqrt{x}}{12\sqrt{x}}=0`

`<=>\frac{4\sqrt{x}-8-3\sqrt{x}}{12\sqrt{x}}=0`

`<=>\frac{\sqrt{x}-8}{12\sqrt{x}}=0`

`=>\sqrt{x}-8=0`

`<=>\sqrt{x}=8`

`<=>x=64(N)`

Vậy `x=64` thì `P=1/4`

c)

Ta có: `x=4+2\sqrt{3}(N)`

`=>P=\frac{\sqrt{4+2\sqrt{3}}-2}{3\sqrt{4+2\sqrt{3}}}`
`<=>P=\frac{\sqrt{2(2+\sqrt{3})}-2}{3\sqrt{2(2+\sqrt{3})}}`
`<=>P=\frac{\sqrt{2} \sqrt{2+\sqrt{3}}-2}{3\sqrt{2} \sqrt{2+\sqrt{3}}}`

`<=>P=\frac{\sqrt{2} (\sqrt{2+\sqrt{3}}-\sqrt{2})}{3\sqrt{2} \sqrt{2+\sqrt{3}}}`
`<=>P=\frac{ \sqrt{2+\sqrt{3}}-\sqrt{2}}{3\sqrt{2+\sqrt{3}}}`
`<=>P=\frac{ \sqrt{2+\sqrt{3}}}{3\sqrt{2+\sqrt{3}}}-\frac{ \sqrt{2}}{3\sqrt{2+\sqrt{3}}}`
`<=>P=\frac{1}{3}-\frac{ \sqrt{2}}{3\sqrt{2+\sqrt{3}}}`

Vậy `P=\frac{1}{3}-\frac{ \sqrt{2}}{3\sqrt{2+\sqrt{3}}}≈0,09` tại `x=4+2\sqrt{3}`