`P=((x-\sqrt{x}+2)/(x-\sqrt{x}-2)-(x)/(x-2\sqrt{x})):(1-\sqrt{x})/(2-\sqrt{x})(Đk:x>0;x\ne1;x\ne4)`

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

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

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

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

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

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

Vậy `P=(-2)/(\sqrt{x}+1)` với `x>0;x\ne1;x\ne4`

Đáp án+Giải thích các bước giải:

Đề 1:

 `P=((x-\sqrtx+2)/(x-\sqrtx-2)-x/(x-2\sqrtx)).(1-\sqrtx)/(2-\sqrtx)`

`\to P=((x-\sqrtx+2)/((\sqrtx-2)(\sqrtx+1))-x/(\sqrtx(\sqrtx-2))).(1-\sqrtx)/(2-\sqrtx)`

`\to P=((x-\sqrtx+2).\sqrtx-x(\sqrtx+1))/(\sqrtx(\sqrtx-2)(\sqrtx+1)).(1-\sqrtx)/(2-\sqrtx)`

`\to P=(x\sqrtx-x+2\sqrtx-x\sqrtx-x)/(\sqrtx(\sqrtx-2)(\sqrtx+1)).(1-\sqrtx)/(2-\sqrtx)`

`\to P=(-2x+2\sqrtx)/(\sqrtx(\sqrtx-2)(\sqrtx+1)).(1-\sqrtx)/(2-\sqrtx)`

`\to P=(-2\sqrtx(\sqrtx-1))/(\sqrtx(\sqrtx-2)(\sqrtx+1)).(1-\sqrtx)/(2-\sqrtx)`

`\to P=(-2(\sqrtx-1))/((\sqrtx-2)(\sqrtx+1)).(1-\sqrtx)/(2-\sqrtx)`

`\to P=(-2(\sqrtx-1).(1-\sqrtx))/((\sqrtx-2)(\sqrtx+1)(2-\sqrtx))`

`\to P=(-2(\sqrtx-1)^2)/((\sqrtx-2)^2(\sqrtx+1))`

Đề 2:

 `P=((x-\sqrtx+2)/(x-\sqrtx-2)-x/(x-2\sqrtx)):(1-\sqrtx)/(2-\sqrtx)`

`\to P=((x-\sqrtx+2)/((\sqrtx-2)(\sqrtx+1))-x/(\sqrtx(\sqrtx-2))):(1-\sqrtx)/(2-\sqrtx)`

`\to P=((x-\sqrtx+2).\sqrtx-x(\sqrtx+1))/(\sqrtx(\sqrtx-2)(\sqrtx+1)):(1-\sqrtx)/(2-\sqrtx)`

`\to P=(x\sqrtx-x+2\sqrtx-x\sqrtx-x)/(\sqrtx(\sqrtx-2)(\sqrtx+1)):(1-\sqrtx)/(2-\sqrtx)`

`\to P=(-2x+2\sqrtx)/(\sqrtx(\sqrtx-2)(\sqrtx+1)):(1-\sqrtx)/(2-\sqrtx)`

`\to P=(-2\sqrtx(\sqrtx-1))/(\sqrtx(\sqrtx-2)(\sqrtx+1)).(2-\sqrtx)/(1-\sqrtx)`

`\to P=(-2(\sqrtx-1))/((\sqrtx-2)(\sqrtx+1)).(2-\sqrtx)/(1-\sqrtx)`

`\to P=2/((\sqrtx-2)(\sqrtx+1)).(2-\sqrtx)`

`\to P=-2/((2-\sqrtx)(\sqrtx+1)).(2-\sqrtx)`

`\to P=-2/(\sqrtx+1)`