a: Ta có: \(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\)
\(=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)+\left(\sqrt{2x}+\sqrt{x}\right)\left(\sqrt{2x}+1\right)-\left(2x-1\right)}{2x-1}\)
\(=\frac{x\sqrt2-\sqrt{x}+\sqrt{2x}-1+2x+\sqrt{2x}+x\sqrt2+\sqrt{x}-2x+1}{2x-1}\)
\(=\frac{2x\sqrt2+2\sqrt{2x}}{2x-1}=\frac{2\cdot\sqrt{2x}\left(\sqrt{x}+1\right)}{2x-1}\)
Ta có: \(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\)
\(=\frac{2x-1+\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)-\left(\sqrt{2x}+\sqrt{x}\right)\left(\sqrt{2x}+1\right)}{2x-1}\)
\(=\frac{2x-1+x\sqrt2-\sqrt{x}+\sqrt{2x}-1-2x-\sqrt{2x}-x\sqrt2-\sqrt{x}}{2x-1}\)
\(=\frac{-2\sqrt{x}-2}{2x-1}=\frac{-2\left(\sqrt{x}+1\right)}{2x-1}\)
Ta có: \(A=\left(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right):\left(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right)\)
\(=\frac{2\sqrt{2x}\left(\sqrt{x}+1\right)}{2x-1}\cdot\frac{2x-1}{-2\left(\sqrt{x}+1\right)}=-\sqrt{2x}\)
b: \(2x=2\cdot\frac{3+2\sqrt2}{2}=3+2\sqrt2\)
\(A=-\sqrt{2x}\)
\(=-\sqrt{3+2\sqrt2}=-\sqrt{\left(\sqrt2+1\right)^2}=-\left(\sqrt2+1\right)\)
