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

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Simplify the expression.

Move the negative one from the denominator of $\frac{3 + 2 \sqrt{3}}{- 1}$ .

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

Rewrite $- 1 \cdot (3 + 2 \sqrt{3})$ as $- (3 + 2 \sqrt{3})$ .

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

Step 6

Apply the distributive property.

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

Step 7

Multiply.

Multiply $- 1$ by $3$ .

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

Multiply $2$ by $- 1$ .

$- 3 - 2 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 3 - 2 \sqrt{3}$

Decimal Form:

$- 6.46410161 \dots$