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