Rút gọn biểu thức \(A = \left( {\frac{{x + 3}}{{x - 9}} + \frac{1}{{\sqrt x + 3}}} \right):\frac{{\sqrt x }}{{\sqrt x + 3}}\) (x ≥ 0, x ≠ 9).

Với x ≥ 0, x ≠ 9, ta có:

\(A = \left( {\frac{{x + 3}}{{x - 9}} + \frac{1}{{\sqrt x + 3}}} \right):\frac{{\sqrt x }}{{\sqrt x + 3}}\)

\(A = \left[ {\frac{{\left( {x + 3} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}} + \frac{{\sqrt x - 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}} \right].\frac{{\sqrt x + 3}}{{\sqrt x }}\)

\(A = \frac{{x + \sqrt x }}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}.\frac{{\sqrt x + 3}}{{\sqrt x }}\)

\(A = \frac{{\sqrt x + 1}}{{\sqrt x - 3}}.\)