a, ĐK: \(x\ge0;x\ne1\)
\(P=\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\sqrt{x}-x+\sqrt{x}-1}\right):\left(\dfrac{x+\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}+\dfrac{1}{x+1}\right)\)
\(=\left[\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+1\right)}\right]:\left[\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(x+1\right)}+\dfrac{1}{x+1}\right]\)
\(=\dfrac{x+1-2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+1\right)}:\left(\dfrac{\sqrt{x}}{x+1}+\dfrac{1}{x+1}\right)\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(x+1\right)}:\dfrac{\sqrt{x}+1}{x+1}\)
\(=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)
