a: \(\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{\sqrt{x}+2}{x\cdot\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\)
\(=\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\frac{1}{\sqrt{x}-1}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}-1\right)+\sqrt{x}+2-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{x-\sqrt{x}-x+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{-\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=-\frac{1}{x+\sqrt{x}+1}\)
Ta có: \(M=\left(\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{\sqrt{x}+2}{x\cdot\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\frac{\sqrt{x}-1}{\sqrt{x}}\)
\(=\frac{-1}{x+\sqrt{x}+1}\cdot\frac{\sqrt{x}}{\sqrt{x}-1}=-\frac{\sqrt{x}}{x\sqrt{x}-1}\)
