How do you rationalize the denominator and simplify 12/sqrt13?

$\frac{12 \sqrt{13}}{13}$
To rationalise the denominator for $\frac{a}{\sqrt{b}}$ you multiply by $\frac{\sqrt{b}}{\sqrt{b}}$ since this turns the $\sqrt{b}$ on the bottom into a $b$, and is the same as multiply by $1$.
$\frac{12}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}} = \frac{12 \sqrt{13}}{13}$
Since $\frac{12}{13}$ cannot be simplified, we leave it as $\frac{12 \sqrt{13}}{13}$