Answer
$\dfrac{y+6\sqrt{y}}{y-36}$
Work Step by Step
Multiplying by the conjugate of the denominator and using $(a+b)(a-b)=a^2-b^2,$ the given expression, $
\dfrac{\sqrt{y}}{\sqrt{y}-6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{y}}{\sqrt{y}-6}\cdot\dfrac{\sqrt{y}+6}{\sqrt{y}+6}
\\\\=
\dfrac{\sqrt{y}(\sqrt{y}+6)}{(\sqrt{y})^2-(6)^2}
\\\\=
\dfrac{y+6\sqrt{y}}{y-36}
.\end{array}
