Cho \(P = 1 + \left( { \frac{{2x + \sqrt x - 1}}{{1 - x}} - \frac{{2x \sqrt x - \sqrt x + x}}{{1 - x \sqrt x }}} \right). \frac{{x - \sqrt x }}{{2 \sqrt x - 1}} \) với \(x \ge 0,x \ne 1,x \ne \frac{1}{4} \). Rút gọn \(P \). Tìm các giá trị của \(x \) sao cho \(P = \frac{4}{5} \).
A.\(P = \frac{{\sqrt x + 1}}{{x + \sqrt x + 1}}\,\,\,;\,\,\,\,\left[ \begin{array}{l}x = 7 + 2\sqrt 3 \\x = 7 - 2\sqrt 3 \end{array} \right.\)
B.\(P = \frac{{x + 1}}{{x - \sqrt x + 1}}\,\,\,;\,\,\,\,\left[ \begin{array}{l}x = 5 + 2\sqrt 3 \\x = 5 - 2\sqrt 3 \end{array} \right.\)
C.\(P = \frac{{\sqrt x + 1}}{{x - \sqrt x + 1}}\,\,\,;\,\,\,\,\left[ \begin{array}{l}x = 5 + 4\sqrt 3 \\x = 5 - 4\sqrt 3 \end{array} \right.\)
D.\(P = \frac{{x + 1}}{{x + \sqrt x + 1}}\,\,\,;\,\,\,\,\left[ \begin{array}{l}x = 7 + 4\sqrt 3 \\x = 7 - 4\sqrt 3 \end{array} \right.\)