Đáp án:

 `P=1`

Giải thích các bước giải:

 `P=(\frac{2}{\sqrt{x}+1}-\frac{1}{\sqrt{x}-1}+\frac{3\sqrt{x}-1}{x-1}):\frac{4}{\sqrt{x}+1}`

`(đk:x\ge0;x\ne1)`

`=[\frac{2.(\sqrt{x}-1)}{(\sqrt{x}-1).(\sqrt{x}+1)}-\frac{\sqrt{x}+1}{(\sqrt{x}-1).(\sqrt{x}+1)}+\frac{3\sqrt{x}-1}{(\sqrt{x}-1).(\sqrt{x}+1)}].(\frac{\sqrt{x}+1}{4})`

`=[\frac{2\sqrt{x}-2-\sqrt{x}-1+3\sqrt{x}-1}{(\sqrt{x}-1).(\sqrt{x}+1)}]. (\frac{\sqrt{x}+1}{4})`

`=[\frac{4\sqrt{x}-4}{(\sqrt{x}-1).(\sqrt{x}+1)}].(\frac{\sqrt{x}+1}{4})`

`=[\frac{4.(\sqrt{x}-1)}{(\sqrt{x}-1).(\sqrt{x}+1)}].(\frac{\sqrt{x}+1}{4})`

`=(\frac{4}{\sqrt{x}+1}).(\frac{\sqrt{x}+1}{4})`

`=1`

Vậy `P=1` với `x\ge0;x\ne1.`