Trigonometry Examples

$\frac{6}{3 + \sqrt{3}}$

Step 1

Multiply $\frac{6}{3 + \sqrt{3}}$ by $\frac{3 - \sqrt{3}}{3 - \sqrt{3}}$ .

$\frac{6}{3 + \sqrt{3}} \cdot \frac{3 - \sqrt{3}}{3 - \sqrt{3}}$

Step 2

Multiply $\frac{6}{3 + \sqrt{3}}$ by $\frac{3 - \sqrt{3}}{3 - \sqrt{3}}$ .

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Cancel the common factor of $6$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $3 - \sqrt{3}$ by $1$ .

$3 - \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$3 - \sqrt{3}$

Decimal Form:

$1.26794919 \dots$