Simplify -2/(1+ square root of 6)

$\frac{- 2}{1 + \sqrt{6}}$

Step 1

Move the negative in front of the fraction.

$- \frac{2}{1 + \sqrt{6}}$

Step 2

Multiply $\frac{2}{1 + \sqrt{6}}$ by $\frac{1 - \sqrt{6}}{1 - \sqrt{6}}$ .

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

Step 3

Multiply $\frac{2}{1 + \sqrt{6}}$ by $\frac{1 - \sqrt{6}}{1 - \sqrt{6}}$ .

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

Step 4

Expand the denominator using the FOIL method.

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

Step 5

Simplify.

$- \frac{2 (1 - \sqrt{6})}{- 5}$

Step 6

Move the negative in front of the fraction.

$- - \frac{2 (1 - \sqrt{6})}{5}$

Step 7

Multiply $- - \frac{2 (1 - \sqrt{6})}{5}$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{2 (1 - \sqrt{6})}{5}$

Multiply $\frac{2 (1 - \sqrt{6})}{5}$ by $1$ .

$\frac{2 (1 - \sqrt{6})}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2 (1 - \sqrt{6})}{5}$

Decimal Form:

$- 0.57979589 \dots$