A\(=\left(\dfrac{\sqrt{x}-2}{x-1}-\dfrac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right).\dfrac{x^2-2x+1}{2}\)
A\(=\left(\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}+2}{\left(\sqrt{x}+1\right)^2}\right).\dfrac{\left(x-1\right)^2}{2}\)
A\(=\left(\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2}\right).\dfrac{\left(x-1\right)^2}{2}\)
A\(=\left(\dfrac{\left(x+\sqrt{x}-2\sqrt{x}-2\right)-\left(x-\sqrt{x}+2\sqrt{x}-2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)}\right)\dfrac{\left(x-1\right)^2}{2}\)
A\(=\left(\dfrac{x-\sqrt{x}-2-x-\sqrt{x}-\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)}\right)\dfrac{\left(x-1\right)^2}{2}\)
A\(=\left(-\dfrac{2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)}\right)\dfrac{\left(x-1\right)^2}{2}\)
A=\(-\dfrac{2\sqrt{x}.\left(\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right).2}\)
A\(=-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)^2\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)}\)
A\(=-\sqrt{x}\left(\sqrt{x}-1\right)\)
A\(=-x+\sqrt{x}\)
