`A=(sqrtx-1)/(sqrtx+1)-(sqrtx+3)/(sqrtx-2)-(x+5)/(x-sqrtx-2)`
`đk:x>=0,x ne 4`
`A=((sqrtx-1)(sqrtx-2)-(sqrtx+3)(sqrtx+1)-x-5)/(x-sqrtx-2)`
`=(x-3sqrtx+2-x-4sqrtx-3-x-5)/(x-sqrtx-2)`
`=(-x-7sqrtx-6)/(x-sqrtx-2)`
`=(-(sqrtx+1)(sqrtx+6))/((sqrtx+1)(sqrtx-2))`
`=(-(sqrtx+6))/(sqrtx-2)`
Ta có: \(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+3}{\sqrt{x}-2}-\dfrac{x+5}{x-\sqrt{x}-2}\)
\(=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}-\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}-\dfrac{x+5}{\left(\sqrt{x}-2\right)\cdot\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x-3\sqrt{x}+2-x-4\sqrt{x}-3-x-5}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{-x-7\sqrt{x}-6}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{-\sqrt{x}-6}{\sqrt{x}-2}\)
