Simplify 12/( square root of 6+ square root of 2)

$\frac{12}{\sqrt{6} + \sqrt{2}}$

Multiply $\frac{12}{\sqrt{6} + \sqrt{2}}$ by $\frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}$ .

$\frac{12}{\sqrt{6} + \sqrt{2}} \cdot \frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}$

Multiply $\frac{12}{\sqrt{6} + \sqrt{2}}$ by $\frac{\sqrt{6} - \sqrt{2}}{\sqrt{6} - \sqrt{2}}$ .

$\frac{12 (\sqrt{6} - \sqrt{2})}{(\sqrt{6} + \sqrt{2}) (\sqrt{6} - \sqrt{2})}$

Expand the denominator using the FOIL method.

$\frac{12 (\sqrt{6} - \sqrt{2})}{{\sqrt{6}}^{2} - \sqrt{12} + \sqrt{12} - {\sqrt{2}}^{2}}$

Simplify.

$\frac{12 (\sqrt{6} - \sqrt{2})}{4}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12 (\sqrt{6} - \sqrt{2})$ .

$\frac{4 (3 (\sqrt{6} - \sqrt{2}))}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (3 (\sqrt{6} - \sqrt{2}))}{4 (1)}$

Cancel the common factor.

$\frac{4 (3 (\sqrt{6} - \sqrt{2}))}{4 \cdot 1}$

Rewrite the expression.

$\frac{3 (\sqrt{6} - \sqrt{2})}{1}$

Divide $3 (\sqrt{6} - \sqrt{2})$ by $1$ .

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

Apply the distributive property.

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

Multiply $- 1$ by $3$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.10582854 \dots$