Trigonometry Examples

$\frac{9}{9 + \sqrt{5}}$

Step 1

Multiply $\frac{9}{9 + \sqrt{5}}$ by $\frac{9 - \sqrt{5}}{9 - \sqrt{5}}$ .

$\frac{9}{9 + \sqrt{5}} \cdot \frac{9 - \sqrt{5}}{9 - \sqrt{5}}$

Step 2

Multiply $\frac{9}{9 + \sqrt{5}}$ by $\frac{9 - \sqrt{5}}{9 - \sqrt{5}}$ .

$\frac{9 (9 - \sqrt{5})}{(9 + \sqrt{5}) (9 - \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{9 (9 - \sqrt{5})}{81 - 9 \sqrt{5} + \sqrt{5} \cdot 9 - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{9 (9 - \sqrt{5})}{76}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9 (9 - \sqrt{5})}{76}$

Decimal Form:

$0.80099195 \dots$