Precalculus Examples

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

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

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

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

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

Apply the distributive property.

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

Multiply.

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Multiply $3$ by $2$ .

$6 + 3 (- \sqrt{3})$

Multiply $- 1$ by $3$ .

$6 - 3 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$6 - 3 \sqrt{3}$

Decimal Form:

$0.80384757 \dots$