\(P=\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}+\dfrac{2\sqrt{x}}{\sqrt{x}-1}-\dfrac{3\sqrt{x}-1}{1-x}\right)\left(\dfrac{2}{\sqrt{x}}-\dfrac{2}{x}\right)\left(x>0,x\ne1\right)\)
\(=\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}+\dfrac{2\sqrt{x}}{\sqrt{x}-1}+\dfrac{3\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right).\dfrac{2\sqrt{x}-2}{x}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2+2\sqrt{x}\left(\sqrt{x}+1\right)+3\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{2\left(\sqrt{x}-1\right)}{x}\)
\(=\dfrac{3x+3\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{2\left(\sqrt{x}-1\right)}{x}=\dfrac{3\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{2\left(\sqrt{x}-1\right)}{x}\)
\(=\dfrac{6}{\sqrt{x}}\)
Ta có: \(P=\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}+\dfrac{2\sqrt{x}}{\sqrt{x}-1}-\dfrac{3\sqrt{x}-1}{1-x}\right)\cdot\left(\dfrac{2}{\sqrt{x}}-\dfrac{2}{x}\right)\)
\(=\dfrac{x-2\sqrt{x}+1+2x+2\sqrt{x}+3\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\cdot\dfrac{2\sqrt{x}-2}{x}\)
\(=\dfrac{3x+3\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\cdot\dfrac{2\sqrt{x}-2}{x}\)
\(=\dfrac{3\sqrt{x}\left(\sqrt{x}+1\right)\cdot2\cdot\left(\sqrt{x}-1\right)}{x\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{6}{\sqrt{x}}\)
