\[\frac{12}{\sqrt{5} - 1} = \frac{12\left( \sqrt{5} + 1 \right)}{\left( \sqrt{5} - 1 \right)\left( \sqrt{5} + 1 \right)} =\]
\[= \frac{12\left( \sqrt{5} + 1 \right)}{5 - 1} = \frac{12\left( \sqrt{5} + 1 \right)}{4} = 3\left( \sqrt{5} + 1 \right)\]