Đáp án:

Giải thích các bước giải:

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

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

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

`=`$\frac{x^2-\sqrt[]{x}}{x+\sqrt[]{x}+1}$ `-2`$\sqrt[]{x}$`+1+2`$\sqrt[]{x}$`+2`

`=`$\frac{x^2-\sqrt[]{x}}{x+\sqrt[]{x}+1}$ `+3`

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

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

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

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

`=x-`$\sqrt[]{x}$`+3`

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