`2)B=(sqrtx+1)/(x-1)-(x+2)/(xsqrtx-1)-(sqrtx+1)/(x+sqrtx+1)(x>0,x ne 1)`
`=(sqrtx+1)/(x-1)-(x+2)/(xsqrtx-1)-(x-1)/(xsqrtx-1)`
`=(sqrtx+1)/(x-1)-(x+2+x-1)/(xsqrtx-1)`
`=(sqrtx+1)/(x-1)-(2x+1)/(xsqrtx-1)`
`=((sqrtx+1)(x+sqrtx+1)-(2x+1)(sqrtx+1))/((x-1)(x-sqrtx+1))`
`=(xsqrtx+2x+2sqrtx+1-2xsqrtx-2x-sqrtx-1)/((x-1)(x-sqrtx+1))`
`=(-xsqrtx+sqrtx)/((x-1)(x-sqrtx+1))`
`=(-sqrtx(x-1))/((x-1)(x-sqrtx+1))`
`=-sqrtx/(x-sqrtx+1)`
Cách khác:
2) Ta có: \(B=\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\dfrac{1}{\sqrt{x}-1}-\dfrac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\dfrac{x+\sqrt{x}+1-x-2-\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}-1-x+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{-\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=-\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\)
2b) \(\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{x+2}{\left(\sqrt{x}\right)^3-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\dfrac{\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)-\left(x+2\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}+1\right)\left(x-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{x\sqrt{x}+2x+2\sqrt{x}+1-x\sqrt{x}-x-2\sqrt{x}-2-x\sqrt{x}+\sqrt{x}-x+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{-x\sqrt{x}+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}=\dfrac{-\sqrt{x}\left(x-1\right)}{\left(x-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{-\sqrt{x}}{x+\sqrt{x}+1}\)
