a: \(\left(\dfrac{2x+\sqrt{x}-1}{1-x}-\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1-x\sqrt{x}}\right)\cdot\dfrac{x-\sqrt{x}}{2\sqrt{x}-1}\)
\(=\left(\dfrac{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right)\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{2\sqrt{x}-1}\)
\(=\dfrac{\left(-2\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)+2x\sqrt{x}+x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{2\sqrt{x}-1}\)
\(=\dfrac{-\left(x+\sqrt{x}+1\right)+\sqrt{x}\left(\sqrt{x}+1\right)}{x-\sqrt{x}+1}\cdot\dfrac{\sqrt{x}}{1}\)
\(=\dfrac{-x-\sqrt{x}-1+x+\sqrt{x}}{x-\sqrt{x}+1}\cdot\sqrt{x}=\dfrac{\sqrt{x}}{x-\sqrt{x}+1}\)
\(A=1+\dfrac{\sqrt{x}}{x-\sqrt{x}+1}=\dfrac{x+1}{x-\sqrt{x}+1}\)
c: \(A-\dfrac{2}{3}=\dfrac{3x+3-2x+2\sqrt{x}-2}{3\left(x-\sqrt{x}+1\right)}=\dfrac{\left(\sqrt{x}+1\right)^2}{3\left(x-\sqrt{x}+1\right)}>0\)
=>A>2/3
