Trigonometry Examples

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

Step 1

Cancel the common factor of $5$ and $- 5 - 5 \sqrt{3}$ .

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Step 1.1

Factor $5$ out of $5$ .

$\frac{5 (1)}{- 5 - 5 \sqrt{3}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $- 5$ .

$\frac{5 \cdot 1}{5 \cdot - 1 - 5 \sqrt{3}}$

Step 1.2.2

Factor $5$ out of $- 5 \sqrt{3}$ .

$\frac{5 \cdot 1}{5 \cdot - 1 + 5 (- \sqrt{3})}$

Step 1.2.3

Factor $5$ out of $5 (- 1) + 5 (- \sqrt{3})$ .

$\frac{5 \cdot 1}{5 (- 1 - \sqrt{3})}$

Step 1.2.4

Cancel the common factor.

$\frac{5 \cdot 1}{5 (- 1 - \sqrt{3})}$

Step 1.2.5

Rewrite the expression.

$\frac{1}{- 1 - \sqrt{3}}$

Step 2

Multiply $\frac{1}{- 1 - \sqrt{3}}$ by $\frac{- 1 + \sqrt{3}}{- 1 + \sqrt{3}}$ .

$\frac{1}{- 1 - \sqrt{3}} \cdot \frac{- 1 + \sqrt{3}}{- 1 + \sqrt{3}}$

Step 3

Multiply $\frac{1}{- 1 - \sqrt{3}}$ by $\frac{- 1 + \sqrt{3}}{- 1 + \sqrt{3}}$ .

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

Step 4

Expand the denominator using the FOIL method.

$\frac{- 1 + \sqrt{3}}{1 - \sqrt{3} + \sqrt{3} - {\sqrt{3}}^{2}}$

Step 5

Simplify.

$\frac{- 1 + \sqrt{3}}{- 2}$

Step 6

Move the negative in front of the fraction.

$- \frac{- 1 + \sqrt{3}}{2}$

Step 7

Rewrite $- 1$ as $- 1 (1)$ .

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

Step 8

Factor $- 1$ out of $\sqrt{3}$ .

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

Step 9

Factor $- 1$ out of $- 1 (1) - 1 (- \sqrt{3})$ .

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

Step 10

Simplify the expression.

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Step 10.1

Move the negative in front of the fraction.

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

Step 10.2

Multiply $- 1$ by $- 1$ .

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

Step 10.3

Multiply $\frac{1 - \sqrt{3}}{2}$ by $1$ .

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

Step 11

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.36602540 \dots$