Answer
$-\dfrac{20+30\sqrt{3}}{23}$
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{10}{2-3\sqrt{3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{10}{2-3\sqrt{3}}\cdot\dfrac{2+3\sqrt{3}}{2+3\sqrt{3}}
\\\\=
\dfrac{20+30\sqrt{3}}{(2)^2-(3\sqrt{3})^2}
\\\\=
\dfrac{20+30\sqrt{3}}{4-9\cdot3}
\\\\=
\dfrac{20+30\sqrt{3}}{4-27}
\\\\=
\dfrac{20+30\sqrt{3}}{-23}
\\\\=
-\dfrac{20+30\sqrt{3}}{23}
.\end{array}
