rút gọn : $\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}$ - $\frac{-2x +\sqrt{x}}{\sqrt{x}}$ + $\frac{2(x-1)}{\sqrt{x}-1}$

Đáp án+Giải thích các bước giải:

 `\frac{x^{2}-\sqrt{x}}{x+\sqrt{x}+1}-\frac{-2x+\sqrt{x}}{\sqrt{x}}+\frac{2.(x-1)}{\sqrt{x}-1}` `(đk:x>0;x\ne1)`

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

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

`=\frac{\sqrt{x}.(\sqrt{x}-1).(x+\sqrt{x}+1)}{x+\sqrt{x}+1}-(-2\sqrt{x}+1)+2.(\sqrt{x}+1)`

`=\sqrt{x}.(\sqrt{x}-1)+2\sqrt{x}-1+2\sqrt{x}+2`

`=x-\sqrt{x}+4\sqrt{x}+1`

`=3\sqrt{x}+x+1`