The problem asks us to rationalize the denominator of the expression $\frac{1}{\sqrt{3y}}$ and simplify.

1. Problem Description

The problem asks us to rationalize the denominator of the expression $\frac{1}{\sqrt{3y}}$ and simplify.

2. Solution Steps

To rationalize the denominator, we need to eliminate the square root from the denominator. We can do this by multiplying both the numerator and the denominator by $\sqrt{3y}$.

$\frac{1}{\sqrt{3y}} = \frac{1}{\sqrt{3y}} \cdot \frac{\sqrt{3y}}{\sqrt{3y}}$

$\frac{1}{\sqrt{3y}} = \frac{\sqrt{3y}}{(\sqrt{3y})^2}$

$\frac{1}{\sqrt{3y}} = \frac{\sqrt{3y}}{3y}$

3. Final Answer

$\frac{\sqrt{3y}}{3y}$