How do I rationalize the following denominator $$\frac{-2}{3\sqrt\frac{5}{12u}}$$
What I did: 
turned denominator and numerator into square roots
$\frac{\sqrt5}{\sqrt{12u}}$
simplified denominator to
$2\sqrt{3u}$ and $2$ is multiplied by $-2/3$ to make $-4/3 \sqrt 5/\sqrt{12u}$
I then multiplied denominator and numerator by denominator to get
$\frac{4\sqrt{15u}}{9u}$
correct answer: $\frac{-\sqrt{15u}}{9u}$ 
what did i do wrong thanks?

Your 'correct' answer and the other answer are wrong. Please have a look at this: 
$$
\begin{align}
\frac{-2}{3\sqrt\frac{5}{12u}}&=-\frac{2}{3}\times\frac{\sqrt{12u}}{\sqrt{5}}\\\\
&=-\frac{2}{3}\times\frac{\sqrt{5}\times \sqrt{12u}}{\sqrt{5}\times \sqrt{5}}\\\\
&=-\frac{2}{15}\times \sqrt{5}\times \sqrt{12u}\\\\
&=-\frac{2}{15}\times \sqrt{5}\times \sqrt{4\times 3 \times u}\\\\
&=-\frac{4}{15}\sqrt{15\: u}.
\end{align}
$$ Hoping it helps.
