Simplify 3/(-2+ square root of 13)

$\frac{3}{- 2 + \sqrt{13}}$

Multiply $\frac{3}{- 2 + \sqrt{13}}$ by $\frac{- 2 - \sqrt{13}}{- 2 - \sqrt{13}}$ .

$\frac{3}{- 2 + \sqrt{13}} \cdot \frac{- 2 - \sqrt{13}}{- 2 - \sqrt{13}}$

Multiply $\frac{3}{- 2 + \sqrt{13}}$ by $\frac{- 2 - \sqrt{13}}{- 2 - \sqrt{13}}$ .

$\frac{3 (- 2 - \sqrt{13})}{(- 2 + \sqrt{13}) (- 2 - \sqrt{13})}$

Expand the denominator using the FOIL method.

$\frac{3 (- 2 - \sqrt{13})}{4 + 2 \sqrt{13} + \sqrt{13} \cdot - 2 - {\sqrt{13}}^{2}}$

Simplify.

$\frac{3 (- 2 - \sqrt{13})}{- 9}$

Cancel the common factors.

Factor $3$ out of $- 9$ .

$\frac{3 (- 2 - \sqrt{13})}{3 \cdot - 3}$

Cancel the common factor.

$\frac{3 (- 2 - \sqrt{13})}{3 \cdot - 3}$

Rewrite the expression.

$\frac{- 2 - \sqrt{13}}{- 3}$

Move the negative in front of the fraction.

$- \frac{- 2 - \sqrt{13}}{3}$

Rewrite $- 2$ as $- 1 (2)$ .

$- \frac{- 1 (2) - \sqrt{13}}{3}$

Factor $- 1$ out of $- \sqrt{13}$ .

$- \frac{- 1 (2) - (\sqrt{13})}{3}$

Factor $- 1$ out of $- 1 (2) - (\sqrt{13})$ .

$- \frac{- 1 (2 + \sqrt{13})}{3}$

Simplify the expression.

Move the negative in front of the fraction.

$- - \frac{2 + \sqrt{13}}{3}$

Multiply $- 1$ by $- 1$ .

$1 \frac{2 + \sqrt{13}}{3}$

Multiply $\frac{2 + \sqrt{13}}{3}$ by $1$ .

$\frac{2 + \sqrt{13}}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 + \sqrt{13}}{3}$

Decimal Form:

$1.86851709 \dots$