## Elementary Algebra

$\dfrac{y+6\sqrt{y}}{y-36}$
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}