Answer
$\displaystyle \frac{3\sqrt{3y}}{xy}$
Work Step by Step
Simpify the denominator using
$\sqrt[n]{a}\times\sqrt[n]{b}=\sqrt[n]{ab},\qquad$ and
$\sqrt[n]{a^{n}}=(\sqrt[n]{a})^{n}=a$ (for positive a).
$\sqrt{3x^{2}y}=\sqrt{x^{2}\times 3y}=\sqrt{x^{2}}\times\sqrt{3y} = x\sqrt{3y}$
$... =\displaystyle \frac{9}{x\sqrt{3y}}$ $\displaystyle \color{red}{ \cdot\frac{\sqrt{3y}}{\sqrt{3y}} }\qquad$ (rationalize)
$=\displaystyle \frac{9\sqrt{3y}}{x(\sqrt{3y})^{2}}$
$=\displaystyle \frac{9\sqrt{3y}}{x(3y)}$ $\qquad$ ... reduce 3, the common factor
= $\displaystyle \frac{3\sqrt{3y}}{xy}$
