Simplify 2/(4+4 square root of 3)

$\frac{2}{4 + 4 \sqrt{3}}$

Step 1

Cancel the common factor of $2$ and $4 + 4 \sqrt{3}$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot 1}{2 \cdot 2 + 4 \sqrt{3}}$

Factor $2$ out of $4 \sqrt{3}$ .

$\frac{2 \cdot 1}{2 \cdot 2 + 2 (2 \sqrt{3})}$

Factor $2$ out of $2 (2) + 2 (2 \sqrt{3})$ .

$\frac{2 \cdot 1}{2 (2 + 2 \sqrt{3})}$

Cancel the common factor.

$\frac{2 \cdot 1}{2 (2 + 2 \sqrt{3})}$

Rewrite the expression.

$\frac{1}{2 + 2 \sqrt{3}}$

Step 2

Multiply $\frac{1}{2 + 2 \sqrt{3}}$ by $\frac{2 - 2 \sqrt{3}}{2 - 2 \sqrt{3}}$ .

$\frac{1}{2 + 2 \sqrt{3}} \cdot \frac{2 - 2 \sqrt{3}}{2 - 2 \sqrt{3}}$

Step 3

Multiply $\frac{1}{2 + 2 \sqrt{3}}$ by $\frac{2 - 2 \sqrt{3}}{2 - 2 \sqrt{3}}$ .

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

Step 4

Expand the denominator using the FOIL method.

$\frac{2 - 2 \sqrt{3}}{4 - 4 \sqrt{3} + 4 \sqrt{3} - 4 {\sqrt{3}}^{2}}$

Step 5

Simplify.

$\frac{2 - 2 \sqrt{3}}{- 8}$

Step 6

Cancel the common factor of $2 - 2 \sqrt{3}$ and $- 8$ .

Factor $2$ out of $2$ .

$\frac{2 (1) - 2 \sqrt{3}}{- 8}$

Factor $2$ out of $- 2 \sqrt{3}$ .

$\frac{2 (1) + 2 (- \sqrt{3})}{- 8}$

Factor $2$ out of $2 (1) + 2 (- \sqrt{3})$ .

$\frac{2 (1 - \sqrt{3})}{- 8}$

Cancel the common factors.

Factor $2$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1 - \sqrt{3}}{- 4}$

Step 7

Move the negative in front of the fraction.

$- \frac{1 - \sqrt{3}}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{1 - \sqrt{3}}{4}$

Decimal Form:

$0.18301270 \dots$

Simplify 2/(4+4 square root of 3)

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