Algebra Examples

$\frac{3}{\sqrt{x} + \sqrt{5}}$

Step 1

Multiply $\frac{3}{\sqrt{x} + \sqrt{5}}$ by $\frac{\sqrt{x} - \sqrt{5}}{\sqrt{x} - \sqrt{5}}$ .

$\frac{3}{\sqrt{x} + \sqrt{5}} \cdot \frac{\sqrt{x} - \sqrt{5}}{\sqrt{x} - \sqrt{5}}$

Step 2

Multiply $\frac{3}{\sqrt{x} + \sqrt{5}}$ by $\frac{\sqrt{x} - \sqrt{5}}{\sqrt{x} - \sqrt{5}}$ .

$\frac{3 (\sqrt{x} - \sqrt{5})}{(\sqrt{x} + \sqrt{5}) (\sqrt{x} - \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (\sqrt{x} - \sqrt{5})}{{\sqrt{x}}^{2} - \sqrt{x \cdot 5} + \sqrt{5 x} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{3 (\sqrt{x} - \sqrt{5})}{x - 5}$