`P=((\sqrt{x}-2)/(x-1)-(\sqrt{x}+2)/(x+2\sqrt{x}+1))*(1-x)^2/2(x>=0,x\ne1)`

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

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

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

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

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

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

`=-\sqrt{x}(\sqrt{x}-1)`

`=-x+\sqrt{x}`