Answer
$\frac{y\sqrt{3}-y\sqrt{y}}{3-y}$
Work Step by Step
We simplify the fraction by multiplying through by $\sqrt{3}-\sqrt{y}$ and using the fact that $(a-b)(a+b)=a^2-b^2$:
$\displaystyle \frac{y}{\sqrt{3}+\sqrt{y}}=\frac{y}{\sqrt{3}+\sqrt{y}} \displaystyle \frac{\sqrt{3}-\sqrt{y}}{\sqrt{3}-\sqrt{y}}=\frac{y(\sqrt{3}-\sqrt{y})}{3-y}=\frac{y\sqrt{3}-y\sqrt{y}}{3-y}$
