Đáp án:
$\begin{array}{l}
a)\dfrac{{{x^2} - 5}}{{x + \sqrt 5 }}\\
= \dfrac{{\left( {x + \sqrt 5 } \right)\left( {x - \sqrt 5 } \right)}}{{x + \sqrt 5 }}\\
= x - \sqrt 5 \\
b)\dfrac{{{x^2} - 2\sqrt 2 x + 2}}{{{x^2} - 2}}\\
= \dfrac{{{{\left( {x - \sqrt 2 } \right)}^2}}}{{\left( {x - \sqrt 2 } \right)\left( {x + \sqrt 2 } \right)}}\\
= \dfrac{{x - \sqrt 2 }}{{x + \sqrt 2 }}\\
c)4\sqrt x - \dfrac{{\left( {x + 6\sqrt x + 9} \right)\left( {\sqrt x - 3} \right)}}{{x - 9}}\\
= 4\sqrt x - \dfrac{{{{\left( {\sqrt x + 3} \right)}^2}\left( {\sqrt x - 3} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 3} \right)}}\\
= 4\sqrt x - \left( {\sqrt x + 3} \right)\\
= 3\sqrt x - 3\\
d)3\sqrt {9{a^6}} - 6{a^3}\\
= 3.3\left| {{a^3}} \right| - 6{a^3}\\
= - 9{a^3} - 6{a^3}\left( {do:a < 0} \right)\\
= - 15{a^3}
\end{array}$
