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

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

Step 1

Multiply $\frac{4}{2 \sqrt{3} + 3}$ by $\frac{2 \sqrt{3} - 3}{2 \sqrt{3} - 3}$ .

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

Step 2

Multiply $\frac{4}{2 \sqrt{3} + 3}$ by $\frac{2 \sqrt{3} - 3}{2 \sqrt{3} - 3}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (2 \sqrt{3} - 3)}{4 {\sqrt{3}}^{2} - 6 \sqrt{3} + 6 \sqrt{3} - 9}$

Step 4

Simplify.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.61880215 \dots$