Simplify -1/(2- square root of 15)

$\frac{- 1}{2 - \sqrt{15}}$

Step 1

Move the negative in front of the fraction.

$- \frac{1}{2 - \sqrt{15}}$

Step 2

Multiply $\frac{1}{2 - \sqrt{15}}$ by $\frac{2 + \sqrt{15}}{2 + \sqrt{15}}$ .

$- (\frac{1}{2 - \sqrt{15}} \cdot \frac{2 + \sqrt{15}}{2 + \sqrt{15}})$

Step 3

Multiply $\frac{1}{2 - \sqrt{15}}$ by $\frac{2 + \sqrt{15}}{2 + \sqrt{15}}$ .

$- \frac{2 + \sqrt{15}}{(2 - \sqrt{15}) (2 + \sqrt{15})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{2 + \sqrt{15}}{4 + 2 \sqrt{15} - 2 \sqrt{15} - {\sqrt{15}}^{2}}$

Step 5

Simplify.

$- \frac{2 + \sqrt{15}}{- 11}$

Step 6

Move the negative in front of the fraction.

$- - \frac{2 + \sqrt{15}}{11}$

Step 7

Multiply $- - \frac{2 + \sqrt{15}}{11}$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{2 + \sqrt{15}}{11}$

Multiply $\frac{2 + \sqrt{15}}{11}$ by $1$ .

$\frac{2 + \sqrt{15}}{11}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2 + \sqrt{15}}{11}$

Decimal Form:

$0.53390757 \dots$