Answer
$-\dfrac{\sqrt{7}+4}{3}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{3}{\sqrt{7}-4}
$ results to
\begin{array}{l}
\dfrac{3}{\sqrt{7}-4}
\cdot
\dfrac{\sqrt{7}+4}{\sqrt{7}+4}
\\\\=
\dfrac{3\sqrt{7}+12}{(\sqrt{7})^2-(4)^2}
\\\\=
\dfrac{3\sqrt{7}+12}{7-16}
\\\\=
\dfrac{3\sqrt{7}+12}{-9}
\\\\=
-\dfrac{\sqrt{7}+4}{3}
.\end{array}