Đáp án+Giải thích các bước giải:
`(x>0;x\ne1)`
`A=((1)/(\sqrt{x}+1)-(2\sqrt{x}-2)/(x\sqrt{x}-\sqrt{x}+x-1)):(\sqrt{x})/(x+\sqrt{x})`
`=((1)/(\sqrt{x}+1)-(2\sqrt{x}-2)/((x\sqrt{x}+x)-(\sqrt{x}+1))):(\sqrt{x})/(x+\sqrt{x})`
`=((1)/(\sqrt{x}+1)-(2\sqrt{x}-2)/(x.(\sqrt{x}+1)-(\sqrt{x}+1))).(x+\sqrt{x})/(\sqrt{x})`
`=((1)/(\sqrt{x}+1)-(2\sqrt{x}-2)/((x-1).(\sqrt{x}+1))).(x+\sqrt{x})/(\sqrt{x})`
`=((1)/(\sqrt{x}+1)-(2(\sqrt{x}-1))/((\sqrt{x}-1)(\sqrt{x}+1).(\sqrt{x}+1))).(\sqrt{x}(\sqrt{x}+1))/(\sqrt{x})`
`=((\sqrt{x}+1)/((\sqrt{x}+1)^2)-(2)/((\sqrt{x}+1)^2)).(\sqrt{x}+1)`
`=(\sqrt{x}+1-2)/((\sqrt{x}+1)^2).(\sqrt{x}+1)`
`=(\sqrt{x}-1)/((\sqrt{x}+1)^2).(\sqrt{x}+1)`
`=(\sqrt{x}-1)/(\sqrt{x}+1)`
Vậy `A=(\sqrt{x}-1)/(\sqrt{x}+1)` với `x>0;x\ne1`
