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

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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

Step 4

Expand the denominator using the FOIL method.

$- \frac{2 (6 + \sqrt{6})}{36 + 6 \sqrt{6} - 6 \sqrt{6} - {\sqrt{6}}^{2}}$

Step 5

Simplify.

$- \frac{2 (6 + \sqrt{6})}{30}$

Step 6

Cancel the common factors.

Factor $2$ out of $30$ .

$- \frac{2 (6 + \sqrt{6})}{2 \cdot 15}$

Cancel the common factor.

$- \frac{2 (6 + \sqrt{6})}{2 \cdot 15}$

Rewrite the expression.

$- \frac{6 + \sqrt{6}}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{6 + \sqrt{6}}{15}$

Decimal Form:

$- 0.56329931 \dots$