\(P=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{8\sqrt{x}}{x-1}\right):\left(\dfrac{\sqrt{x}-x-3}{x-1}-\dfrac{1}{\sqrt{x}-1}\right)\)
\(\Leftrightarrow P=\left(\dfrac{\left(\sqrt{x}+1\right)^2-\left(\sqrt{x}-1\right)^2-8\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right):\left(\dfrac{\sqrt{x}-x-3-\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)
\(\Leftrightarrow P=\left(\dfrac{\left(\sqrt{x}+1+\sqrt{x}-1\right)\left(\sqrt{x}+1-\sqrt{x}+1\right)-8\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right).\left(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{-x-4}\right)\)
\(\Leftrightarrow P=\dfrac{-4\sqrt{x}}{-x-4}=\dfrac{4\sqrt{x}}{x+4}\)
Thay x = \(3+2\sqrt{2}\) ta được :
\(P=\dfrac{4\sqrt{3+2\sqrt{2}}}{3+2\sqrt{2}+4}=\dfrac{4\left(\sqrt{2}+1\right)}{7+2\sqrt{2}}=\dfrac{4\sqrt{2}+4}{7+2\sqrt{2}}\)
\(P=\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{8\sqrt{x}}{x-1}\right):\left(\dfrac{\sqrt{x}-x-3}{x-1}-\dfrac{1}{\sqrt{x}-1}\right)=\dfrac{x+2\sqrt{x}+1-x+2\sqrt{x}-1-8\sqrt{x}}{x-1}:\dfrac{\sqrt{x}-x-3-\sqrt{x}-1}{x-1}=\dfrac{-4\sqrt{x}}{x-1}.\dfrac{x-1}{-x-4}=\dfrac{4\sqrt{x}}{x+4}\left(x\ne4;x\ge0;x\ne1\right)\)
Ta có : \(x=3+2\sqrt{2}=2+2\sqrt{2}+1=\left(\sqrt{2}+1\right)^2\left(TMĐKXĐ\right)\)
\(P=\dfrac{4\left(\sqrt{2}+1\right)}{3+2\sqrt{2}+4}=\dfrac{4+4\sqrt{2}}{7+2\sqrt{2}}\)
