Answer
$\dfrac{12\sqrt{3}+8}{23}$
Work Step by Step
Multiplying the numerator and the denominator by the conjugate of the denominator, the given expression, $
\dfrac{4}{3\sqrt{3}-2}
,$ is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{4}{3\sqrt{3}-2}\cdot\dfrac{3\sqrt{3}+2}{3\sqrt{3}+2}
\\\\&=
\dfrac{4(3\sqrt{3}+2)}{(3\sqrt{3})^2-(2)^2}
&\left( \text{use }(a+b)(a-b)=a^2-b^2 \right)
\\\\&=
\dfrac{12\sqrt{3}+8}{(3\sqrt{3})^2-(2)^2}
&\left( \text{use Distributive Property} \right)
\\\\&=
\dfrac{12\sqrt{3}+8}{27-4}
\\\\&=
\dfrac{12\sqrt{3}+8}{23}
.\end{align*}
Hence, the rationalized-denominator form of the given expression is $
\dfrac{12\sqrt{3}+8}{23}
$.
