Answer
$\dfrac{y-5}{\sqrt{y}-\sqrt{5}}=\sqrt{y}+\sqrt{5}$
Work Step by Step
$\dfrac{y-5}{\sqrt{y}-\sqrt{5}}$
Multiply the numerator and the denominator of the given expression by $\sqrt{y}+\sqrt{5}$, which is the conjugate of the denominator:
$\dfrac{y-5}{\sqrt{y}-\sqrt{5}}\cdot\dfrac{\sqrt{y}+\sqrt{5}}{\sqrt{y}+\sqrt{5}}=\dfrac{(y-5)(\sqrt{y}+\sqrt{5})}{(\sqrt{y}-\sqrt{5})(\sqrt{y}+\sqrt{5})}=...$
Evaluate the operations indicated and simplify:
$...=\dfrac{(y-5)(\sqrt{y}+\sqrt{5})}{(\sqrt{y})^{2}-(\sqrt{5})^{2}}=\dfrac{(y-5)(\sqrt{y}+\sqrt{5})}{y-5}=\sqrt{y}+\sqrt{5}$
