Simplify -2/(3+ square root of 6)

$\frac{- 2}{3 + \sqrt{6}}$

Step 1

Move the negative in front of the fraction.

$- \frac{2}{3 + \sqrt{6}}$

Step 2

Multiply $\frac{2}{3 + \sqrt{6}}$ by $\frac{3 - \sqrt{6}}{3 - \sqrt{6}}$ .

$- (\frac{2}{3 + \sqrt{6}} \cdot \frac{3 - \sqrt{6}}{3 - \sqrt{6}})$

Step 3

Multiply $\frac{2}{3 + \sqrt{6}}$ by $\frac{3 - \sqrt{6}}{3 - \sqrt{6}}$ .

$- \frac{2 (3 - \sqrt{6})}{(3 + \sqrt{6}) (3 - \sqrt{6})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{2 (3 - \sqrt{6})}{9 - 3 \sqrt{6} + \sqrt{6} \cdot 3 - {\sqrt{6}}^{2}}$

Step 5

Simplify.

$- \frac{2 (3 - \sqrt{6})}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 (3 - \sqrt{6})}{3}$

Decimal Form:

$- 0.36700683 \dots$