Simplify 6/(1- square root of 13)

$\frac{6}{1 - \sqrt{13}}$

Multiply $\frac{6}{1 - \sqrt{13}}$ by $\frac{1 + \sqrt{13}}{1 + \sqrt{13}}$ .

$\frac{6}{1 - \sqrt{13}} \cdot \frac{1 + \sqrt{13}}{1 + \sqrt{13}}$

Multiply $\frac{6}{1 - \sqrt{13}}$ by $\frac{1 + \sqrt{13}}{1 + \sqrt{13}}$ .

$\frac{6 (1 + \sqrt{13})}{(1 - \sqrt{13}) (1 + \sqrt{13})}$

Expand the denominator using the FOIL method.

$\frac{6 (1 + \sqrt{13})}{1 + \sqrt{13} - \sqrt{13} - {\sqrt{13}}^{2}}$

Simplify.

$\frac{6 (1 + \sqrt{13})}{- 12}$

Cancel the common factors.

Factor $6$ out of $- 12$ .

$\frac{6 (1 + \sqrt{13})}{6 \cdot - 2}$

Cancel the common factor.

$\frac{6 (1 + \sqrt{13})}{6 \cdot - 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 2.30277563 \dots$