Rút gọn P. A.\(\frac{{\sqrt x - 3}}{{8\sqrt x - 1}}\) B.\(\frac{{\sqrt x - 3}}{{8\sqrt x }}\) C.\(\frac{{\sqrt x }}{{\sqrt x - 3}}\) D.\(\frac{{\sqrt x }}{{\sqrt x - 3}}\)
Đáp án đúng: B Giải chi tiết: \(P = \left( {\frac{1}{{\sqrt x - 1}} - \frac{1}{{\sqrt x }}} \right):\left( {\frac{{\sqrt x + 1}}{{\sqrt x - 3}} - \frac{{\sqrt x + 3}}{{\sqrt x - 1}}} \right)\) Điều kiện: \(x > 0;x \ne 1\) và \(x \ne 9\). \(\begin{array}{l} = \frac{{\sqrt x - \left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x - 1} \right)\sqrt x }}:\frac{{\left( {\sqrt x + 1} \right)\left( {\sqrt x - 1} \right) - \left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x - 1} \right)}}\\ = \frac{{\sqrt x - \sqrt x + 1}}{{\left( {\sqrt x - 1} \right)\sqrt x }}:\frac{{x - 1 - x + 9}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x - 1} \right)}}\\ = \frac{1}{{\left( {\sqrt x - 1} \right)\sqrt x }}.\frac{{\left( {\sqrt x - 3} \right)\left( {\sqrt x - 1} \right)}}{8}\\ = \frac{{\sqrt x - 3}}{{8\sqrt x }}\end{array}\)