Algebra Examples

$\frac{3}{5 - 2 \sqrt{3}}$

Step 1

Multiply $\frac{3}{5 - 2 \sqrt{3}}$ by $\frac{5 + 2 \sqrt{3}}{5 + 2 \sqrt{3}}$ .

$\frac{3}{5 - 2 \sqrt{3}} \cdot \frac{5 + 2 \sqrt{3}}{5 + 2 \sqrt{3}}$

Step 2

Multiply $\frac{3}{5 - 2 \sqrt{3}}$ by $\frac{5 + 2 \sqrt{3}}{5 + 2 \sqrt{3}}$ .

$\frac{3 (5 + 2 \sqrt{3})}{(5 - 2 \sqrt{3}) (5 + 2 \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 (5 + 2 \sqrt{3})}{25 + 10 \sqrt{3} - 10 \sqrt{3} - 4 {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{3 (5 + 2 \sqrt{3})}{13}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (5 + 2 \sqrt{3})}{13}$

Decimal Form:

$1.95325421 \dots$