GHi nhầm số chứ không phải thiếu.
`P=(x+2)/(xsqrtx+1)+(sqrtx-1)/(x-sqrtx+1)-(sqrtx-1)/(x-1)(x>=0,x ne 1)`
`=(x+2)/((sqrtx+1)(x-sqrtx+1))+(sqrtx-1)/(x-sqrtx+1)-(sqrtx-1)/((sqrtx-1)(sqrtx+1))`
`=(x+2)/((sqrtx+1)(x-sqrtx+1))+((sqrtx-1)(sqrtx+1))/((sqrtx+1)(x-sqrtx+1))-1/(sqrtx+1)`
`(x+2)/((sqrtx+1)(x-sqrtx+1))+((sqrtx-1)(sqrtx+1))/((sqrtx+1)(x-sqrtx+1))-(x-sqrtx+1)/((sqrtx+1)(x-sqrtx+1))`
`=(x+2+x-1-x+sqrtx-1)/((sqrtx+1)(x-sqrtx+1))`
`=(x+sqrtx)/((sqrtx+1)(x-sqrtx+1))`
`=(sqrtx(sqrtx+1))/((sqrtx+1)(x-sqrtx+1))`
`=sqrtx/(x-sqrtx+1)`
Ta có: \(P=\dfrac{x+2}{x\sqrt{x}+1}+\dfrac{\sqrt{x}-1}{x-\sqrt{x}+1}-\dfrac{\sqrt{x}-1}{x-1}\)
\(=\dfrac{x+2}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}+\dfrac{x-1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}-\dfrac{x-\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\)
\(=\dfrac{x+2+x-1-x+\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\)
\(=\dfrac{x+\sqrt{x}}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}}{x-\sqrt{x}+1}\)