Cho \(P = \left( {\frac{{\sqrt x + 1}}{{\sqrt x - 1}} - \frac{{\sqrt x - 1}}{{\sqrt x + 1}} - \frac{{8\sqrt x }}{{x - 1}}} \right):\left( {\frac{{\sqrt x - x - 3}}{{x - 1}} - \frac{1}{{\sqrt x - 1}}} \right)\). Tính giá trị của P khi \(x = 3 + 2\sqrt 2 \).

\(P = \left( {\frac{{{{\left( {\sqrt x + 1} \right)}^2} - {{\left( {\sqrt x - 1} \right)}^2} - 8\sqrt x }}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}} \right):\left( {\frac{{\sqrt x - x - 3 - \sqrt x - 1}}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}} \right)\)

\(P = \left( {\frac{{\left( {\sqrt x + 1 + \sqrt x - 1} \right)\left( {\sqrt x + 1 - \sqrt x + 1} \right) - 8\sqrt x }}{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}} \right).\left( {\frac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right)}}{{ - x - 4}}} \right)\)

\(P = \frac{{ - 4\sqrt x }}{{ - x - 4}} = \frac{{4\sqrt x }}{{x + 4}}\)

Thay \(x = 3 + 2\sqrt 2 \) ta được: \(P = \frac{{4\sqrt {3 + 2\sqrt 2 } }}{{3 + 2\sqrt 2 + 4}} = \frac{{4\left( {\sqrt 2 + 1} \right)}}{{7 + 2\sqrt 2 }} = \frac{{4\sqrt 2 + 4}}{{7 + 2\sqrt 2 }}\).