Đáp án:
$\begin{array}{l}
\dfrac{{a\sqrt a + 27}}{{a - 9}} + \dfrac{{a - 9}}{{{{\left( {\sqrt a - 3} \right)}^2}}}\\
= \dfrac{{\left( {\sqrt a + 3} \right)\left( {a - 3\sqrt a + 9} \right)}}{{\left( {\sqrt a + 3} \right)\left( {\sqrt a - 3} \right)}} + \dfrac{{\left( {\sqrt a - 3} \right)\left( {\sqrt a + 3} \right)}}{{{{\left( {\sqrt a - 3} \right)}^2}}}\\
= \dfrac{{a - 3\sqrt a + 9}}{{\sqrt a - 3}} + \dfrac{{\sqrt a + 3}}{{\sqrt a - 3}}\\
= \dfrac{{a - 2\sqrt a + 12}}{{\sqrt a - 3}}
\end{array}$
