`x\sqrt{x}-1=(\sqrt{x}-1)(x+\sqrt{x}+1)`
`x\sqrt{x}+x+\sqrt{x}=\sqrt{x}(x+\sqrt{x}+1)`
`x^2-\sqrt{x}=\sqrt{x}(x\sqrt{x}-1)=\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)`
`ĐKXXĐ:x>0,x\ne1`
`A={x-2\sqrt{x}}/{x\sqrt{x}-1}+{\sqrt{x}+1}/{x\sqrt{x}+x+\sqrt{x}}+{1+2x-2\sqrt{x}}/{x^2-\sqrt{x}}`
`={x-2\sqrt{x}}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}+{\sqrt{x}+1}/{\sqrt{x}(x+\sqrt{x}+1)}+{1+2x-2\sqrt{x}}/{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}`
`={\sqrt{x}(x-2\sqrt{x})}/{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}+{(\sqrt{x}+1)(\sqrt{x}-1)}/{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}+{1-2x-2\sqrt{x}}/{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}`
`={\sqrt{x}(x-2\sqrt{x})+(\sqrt{x}+1)(\sqrt{x}-1)+1-2x-2\sqrt{x}}/{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}`
`={x\sqrt{x}-2x+x-1+1-2x-2\sqrt{x}}/{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}`
`={x\sqrt{x}-3x-2\sqrt{x}}/{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}`
`={\sqrt{x}(x-3\sqrt{x}-2)}/{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}`
`={x-3\sqrt{x}-2}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}`
`={x-3\sqrt{x}-2}/{x\sqrt{x}-1}`
Vậy với `x>0,x\ne1` thì `A={x-3\sqrt{x}-2}/{x\sqrt{x}-1}`
