Answer
$3\sqrt{6}-3\sqrt{5}$
Work Step by Step
Multiplying by the conjugate of the denominator and using $(a+b)(a-b)=a^2-b^2,$ the given expression, $
\dfrac{3}{\sqrt{6}+\sqrt{5}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3}{\sqrt{6}+\sqrt{5}}\cdot\dfrac{\sqrt{6}-\sqrt{5}}{\sqrt{6}-\sqrt{5}}
\\\\=
\dfrac{3\sqrt{6}-3\sqrt{5}}{(\sqrt{6})^2-(\sqrt{5})^2}
\\\\=
\dfrac{3\sqrt{6}-3\sqrt{5}}{6-5}
\\\\=
\dfrac{3\sqrt{6}-3\sqrt{5}}{1}
\\\\=
3\sqrt{6}-3\sqrt{5}
.\end{array}
