Algebra Examples

$\frac{1}{3 + \sqrt{5}}$

Step 1

Multiply $\frac{1}{3 + \sqrt{5}}$ by $\frac{3 - \sqrt{5}}{3 - \sqrt{5}}$ .

$\frac{1}{3 + \sqrt{5}} \cdot \frac{3 - \sqrt{5}}{3 - \sqrt{5}}$

Step 2

Multiply $\frac{1}{3 + \sqrt{5}}$ by $\frac{3 - \sqrt{5}}{3 - \sqrt{5}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{3 - \sqrt{5}}{9 - 3 \sqrt{5} + \sqrt{5} \cdot 3 - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{3 - \sqrt{5}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 - \sqrt{5}}{4}$

Decimal Form:

$0.19098300 \dots$