(1- $\frac{4}{\sqrt{x}+1 }$ +$\frac{1}{x-1}$ ): $\frac{x-2{\sqrt[]{x}}}{x-1}$ (x>0,x=/1,x=/4) a, rg

Đáp án:

`(\sqrt{x}-2)/(\sqrt{x}).`

Giải thích các bước giải:

`(1-4/(\sqrt{x}+1)+1/(x-1)):(x-2\sqrt{x})/(x-1)(x>=0, x\ne1, x\ne4)`

`=[1-4/(\sqrt{x}+1)+1/((\sqrt{x}-1)(\sqrt{x}+1))]:(\sqrt{x}(\sqrt{x}-2))/(x-1)`

`=[((\sqrt{x}-1)(\sqrt{x}+1))/((\sqrt{x}-1)(\sqrt{x}+1))-(4\sqrt{x}-1)/((\sqrt{x}-1)(\sqrt{x}+1))+1/((\sqrt{x}-1)(\sqrt{x}+1))]:(\sqrt{x}(\sqrt{x}-2))/(x-1)`

`=((\sqrt{x}-1)(\sqrt{x}+1)-4(\sqrt{x}-1)+1)/((\sqrt{x}-1)(\sqrt{x}+1)) :(\sqrt{x}(\sqrt{x}-2))/(x-1)`

`=(x-1-4\sqrt{x}+4+1)/((\sqrt{x}-1)(\sqrt{x}+1)):(\sqrt{x}(\sqrt{x}-2))/(x-1)`

`=(x-4\sqrt{x}+4)/(\sqrt{x^2}-1^2) . (x-1)/(\sqrt{x}(\sqrt{x}-2))`

`=(x-4\sqrt{x}+4)/(\sqrt{x}(\sqrt{x}-2))`

`=((\sqrt{x}-2)^2)/(\sqrt{x}(\sqrt{x}-2))`

`=(\sqrt{x}-2)/(\sqrt{x}).`