# 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.