Simplify -36/(2+ square root of 13)

$\frac{- 36}{2 + \sqrt{13}}$

Move the negative in front of the fraction.

$- \frac{36}{2 + \sqrt{13}}$

Multiply $\frac{36}{2 + \sqrt{13}}$ by $\frac{2 - \sqrt{13}}{2 - \sqrt{13}}$ .

$- (\frac{36}{2 + \sqrt{13}} \cdot \frac{2 - \sqrt{13}}{2 - \sqrt{13}})$

Multiply $\frac{36}{2 + \sqrt{13}}$ by $\frac{2 - \sqrt{13}}{2 - \sqrt{13}}$ .

$- \frac{36 (2 - \sqrt{13})}{(2 + \sqrt{13}) (2 - \sqrt{13})}$

Expand the denominator using the FOIL method.

$- \frac{36 (2 - \sqrt{13})}{4 - 2 \sqrt{13} + \sqrt{13} \cdot 2 - {\sqrt{13}}^{2}}$

Simplify.

$- \frac{36 (2 - \sqrt{13})}{- 9}$

Cancel the common factor of $36$ and $- 9$ .

Factor $9$ out of $36 (2 - \sqrt{13})$ .

$- \frac{9 (4 (2 - \sqrt{13}))}{- 9}$

Move the negative one from the denominator of $\frac{4 (2 - \sqrt{13})}{- 1}$ .

$- (- 1 \cdot (4 (2 - \sqrt{13})))$

Rewrite $- 1 \cdot (4 (2 - \sqrt{13}))$ as $- (4 (2 - \sqrt{13}))$ .

$- - (4 (2 - \sqrt{13}))$

Apply the distributive property.

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

Multiply.

Multiply $4$ by $2$ .

$- - (8 + 4 (- \sqrt{13}))$

Multiply $- 1$ by $4$ .

$- - (8 - 4 \sqrt{13})$

Apply the distributive property.

$- (- 1 \cdot 8 - (- 4 \sqrt{13}))$

Multiply.

Multiply $- 1$ by $8$ .

$- (- 8 - (- 4 \sqrt{13}))$

Multiply $- 4$ by $- 1$ .

$- (- 8 + 4 \sqrt{13})$

Apply the distributive property.

$- - 8 - (4 \sqrt{13})$

Multiply.

Multiply $- 1$ by $- 8$ .

$8 - (4 \sqrt{13})$

Multiply $4$ by $- 1$ .

$8 - 4 \sqrt{13}$

The result can be shown in multiple forms.

Exact Form:

$8 - 4 \sqrt{13}$

Decimal Form:

$- 6.42220510 \dots$