Answer
$\displaystyle \frac{3(\sqrt{5}-4)}{11}=\frac{3\sqrt{5}-12}{11}$
Work Step by Step
We rationalize the denominator:
$\displaystyle \frac{-3}{\sqrt{5}+4}=\frac{-3(\sqrt{5}-4)}{(\sqrt{5}+4)(\sqrt{5}-4)}=\frac{-3(\sqrt{5}-4)}{5-4^2}=\frac{-3(\sqrt{5}-4)}{-11}=\frac{3(\sqrt{5}-4)}{11}=\frac{3\sqrt{5}-12}{11}$
