Đáp án:
\[A = \frac{1}{{\sqrt x - 2}}\]
Giải thích các bước giải:
\(\begin{array}{l}
A = \left( {\frac{{3\sqrt x + 6}}{{x - 4}} + \frac{{\sqrt x }}{{\sqrt x - 2}}} \right):\left( {\frac{{x - 9}}{{\sqrt x - 3}}} \right)\,\,\,\,\,\,\left( {x \ge 0,\,\,x \ne 4;\,\,x \ne 9} \right)\\
= \left( {\frac{{3\left( {\sqrt x + 2} \right)}}{{\left( {\sqrt x - 2} \right)\left( {\sqrt x + 2} \right)}} + \frac{{\sqrt x }}{{\sqrt x - 2}}} \right):\left( {\frac{{\left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right)}}{{\sqrt x - 3}}} \right)\\
= \left( {\frac{3}{{\sqrt x - 2}} + \frac{{\sqrt x }}{{\sqrt x - 2}}} \right):\left( {\sqrt x + 3} \right)\\
= \frac{{\sqrt x + 3}}{{\sqrt x - 2}}.\frac{1}{{\sqrt x + 3}}\\
= \frac{1}{{\sqrt x - 2}}
\end{array}\)
