`***`Lời giải`***`
a)
`P=(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{x-\sqrt{x}}):(\frac{1}{1+\sqrt{x}}+\frac{2}{x-1})`
`=(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{\sqrt{x}(\sqrt{x}-1)}):(\frac{1}{\sqrt{x}+1}+\frac{2}{(\sqrt{x}-1)(\sqrt{x}+1)})`
`=\frac{x-1}{\sqrt{x}(\sqrt{x}-1)}:\frac{\sqrt{x}-1+2}{(\sqrt{x}-1)(\sqrt{x}+1)}`
`=\frac{(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}(\sqrt{x}-1)}:\frac{\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}`
`=\frac{\sqrt{x}+1}{\sqrt{x}}:\frac{1}{\sqrt{x}-1}`
`=\frac{\sqrt{x}+1}{\sqrt{x}}.\sqrt{x}-1`
`=\frac{x-1}{\sqrt{x}}`
b)
Thay $x=8-2\sqrt{7}$ ta có:
`P=\frac{8-2\sqrt{7}-1}{\sqrt{8-2\sqrt{7}}}≈1,04`
c)
Ta có: `P=\frac{x-1}{\sqrt{x}}`
ĐKXĐ: `x\geq0`
Để `P<0` thì `x-1<0<=>x<1`
