Rút gọn biểu thức \(B. \) A.\(B = \frac{{\sqrt x }}{{\sqrt x + 3}}\) B.\(B = \frac{{\sqrt x }}{{\sqrt x - 3}}\) C.\(B = \frac{{\sqrt x - 3}}{{\sqrt x + 3}}\) D.\(B = \frac{{\sqrt x + 3}}{{\sqrt x - 3}}\)
Đáp án đúng: B Giải chi tiết:Điều kiện: \(x \ge 0,\,\,x \ne 9.\) \(\begin{array}{l}B = \frac{{\sqrt x - 1}}{{\sqrt x + 3}} + \frac{{7\sqrt x - 3}}{{x - 9}} = \frac{{\sqrt x - 1}}{{\sqrt x + 3}} + \frac{{7\sqrt x - 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\\,\,\,\, = \frac{{\left( {\sqrt x - 1} \right)\left( {\sqrt x - 3} \right) + 7\sqrt x - 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}} = \frac{{x - 3\sqrt x - \sqrt x + 3 + 7\sqrt x - 3}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}\\\,\,\,\, = \frac{{x + 3\sqrt x }}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}} = \frac{{\sqrt x \left( {\sqrt x + 3} \right)}}{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}} = \frac{{\sqrt x }}{{\sqrt x - 3}}.\end{array}\) Chọn B.