Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

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

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

Step 6

Apply the distributive property.

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

Step 7

Multiply $3$ by $2$ .

$6 + 3 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$6 + 3 \sqrt{3}$

Decimal Form:

$11.19615242 \dots$