Calculus Examples

$\frac{y}{\sqrt{5} + \sqrt{y}}$

Step 1

Multiply $\frac{y}{\sqrt{5} + \sqrt{y}}$ by $\frac{\sqrt{5} - \sqrt{y}}{\sqrt{5} - \sqrt{y}}$ .

$\frac{y}{\sqrt{5} + \sqrt{y}} \cdot \frac{\sqrt{5} - \sqrt{y}}{\sqrt{5} - \sqrt{y}}$

Step 2

Multiply $\frac{y}{\sqrt{5} + \sqrt{y}}$ by $\frac{\sqrt{5} - \sqrt{y}}{\sqrt{5} - \sqrt{y}}$ .

$\frac{y (\sqrt{5} - \sqrt{y})}{(\sqrt{5} + \sqrt{y}) (\sqrt{5} - \sqrt{y})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{y (\sqrt{5} - \sqrt{y})}{{\sqrt{5}}^{2} - \sqrt{5 y} + \sqrt{y \cdot 5} - {\sqrt{y}}^{2}}$

Step 4

Simplify.

$\frac{y (\sqrt{5} - \sqrt{y})}{5 - y}$