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