Trigonometry Examples

$\frac{4}{5 - \sqrt{13}}$

Step 1

Multiply $\frac{4}{5 - \sqrt{13}}$ by $\frac{5 + \sqrt{13}}{5 + \sqrt{13}}$ .

$\frac{4}{5 - \sqrt{13}} \cdot \frac{5 + \sqrt{13}}{5 + \sqrt{13}}$

Step 2

Multiply $\frac{4}{5 - \sqrt{13}}$ by $\frac{5 + \sqrt{13}}{5 + \sqrt{13}}$ .

$\frac{4 (5 + \sqrt{13})}{(5 - \sqrt{13}) (5 + \sqrt{13})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (5 + \sqrt{13})}{25 + 5 \sqrt{13} - 5 \sqrt{13} - {\sqrt{13}}^{2}}$

Step 4

Simplify.

$\frac{4 (5 + \sqrt{13})}{12}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $4$ out of $12$ .

$\frac{4 (5 + \sqrt{13})}{4 \cdot 3}$

Step 5.2

Cancel the common factor.

$\frac{4 (5 + \sqrt{13})}{4 \cdot 3}$

Step 5.3

Rewrite the expression.

$\frac{5 + \sqrt{13}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5 + \sqrt{13}}{3}$

Decimal Form:

$2.86851709 \dots$