Cho hai biểu thức \(A = \dfrac{{\sqrt x }}{{\sqrt x  + 3}}\) và \(B = \dfrac{{2\sqrt x }}{{\sqrt x  - 3}} - \dfrac{{3x + 9}}{{x - 9}}\) với \(x \ge 0,\,\,x \ne 9\).

Rút gọn \(A + B\) ta được:

Điều kiện: \(x \ge 0,\,\,x \ne 9.\)

\(\begin{array}{l}A + B = \dfrac{{\sqrt x }}{{\sqrt x  + 3}} + \dfrac{{2\sqrt x }}{{\sqrt x  - 3}} - \dfrac{{3x + 9}}{{x - 9}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{{\sqrt x }}{{\sqrt x  + 3}} + \dfrac{{2\sqrt x }}{{\sqrt x  - 3}} - \dfrac{{3x + 9}}{{\left( {\sqrt x  - 3} \right)\left( {\sqrt x  + 3} \right)}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{{\sqrt x \left( {\sqrt x  - 3} \right) + 2\sqrt x \left( {\sqrt x  + 3} \right) - 3x - 9}}{{\left( {\sqrt x  - 3} \right)\left( {\sqrt x  + 3} \right)}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{{x - 3\sqrt x  + 2x + 6\sqrt x  - 3x - 9}}{{\left( {\sqrt x  - 3} \right)\left( {\sqrt x  + 3} \right)}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{{3\sqrt x  - 9}}{{\left( {\sqrt x  - 3} \right)\left( {\sqrt x  + 3} \right)}}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{{3\left( {\sqrt x  - 3} \right)}}{{\left( {\sqrt x  - 3} \right)\left( {\sqrt x  + 3} \right)}}\\\,\,\,\,\,\,\,\,\,\,\,\,\, = \dfrac{3}{{\sqrt x  + 3}}\end{array}\)

Vậy \(A + B = \dfrac{3}{{\sqrt x  + 3}}\) (với \(x \ge 0,\,\,x \ne 9\)).