`A=(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+\sqrt{2}x+1}):(\frac{2}{x^2-2x+1})`
`<=> A=(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{(\sqrt{x}+1)^2)).(\frac{(x-1)^2}{2})`
`<=> A=(\frac{(\sqrt{x}-2)(\sqrt{x}+1)^2-(\sqrt{x}+2)(x-1)}{(x-1)(\sqrt{x}+1)^2)).\frac{(x-1)^2}{2}`
`<=> A=( \frac{(\sqrt{x}-2)(\sqrt{x}+1)^2-(\sqrt{x}+2)(\sqrt{x}-1)(\sqrt{x}+1)}{(\sqrt{x}+1)^2}).\frac{x-1}{2}`
`<=> A=\frac{(\sqrt{x}+1)[(\sqrt{x}-2)(\sqrt{x}+1)-(\sqrt{x}+2)(\sqrt{x}-1)]}{(\sqrt{x}+1)^2}.\frac{x-1}{2}`
`<=> A=\frac{x-\sqrt{x}-2-x-\sqrt{x}+2}{\sqrt{x}+1}.\frac{x-1}{2}`
`<=> A=\frac{-2\sqrt{x}}{\sqrt{x}+1}.\frac{x-1}{2}`
`<=> A=\frac{-\sqrt{x}(\sqrt{x}-1)(\sqrt{x}+1)}{\sqrt{x}+1}`
`<=> A=-\sqrt{x}.(\sqrt{x}-1)=-x+\sqrt{x}`
