Đáp án+Giải thích các bước giải:

`H=\frac{x\sqrt{x}+1}{x-1}-\frac{x-1}{\sqrt{x}+1}`

`(đk: x\ge0;x\ne1)`

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

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

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

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

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

`=\frac{\sqrt{x}}{\sqrt{x}-1}`

Vậy `H=\frac{\sqrt{x}}{\sqrt{x}-1}` với `x\ge0;x\ne1`