Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (- 5 + 3 \sqrt{3})}{25 - 15 \sqrt{3} + 15 \sqrt{3} - 9 {\sqrt{3}}^{2}}$

Step 4

Simplify.

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

Step 5

Move the negative in front of the fraction.

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

Step 6

Rewrite $- 5$ as $- 1 (5)$ .

$- \frac{5 (- 1 (5) + 3 \sqrt{3})}{2}$

Step 7

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

$- \frac{5 (- 1 (5) - (- 3 \sqrt{3}))}{2}$

Step 8

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

$- \frac{5 (- 1 (5 - 3 \sqrt{3}))}{2}$

Step 9

Simplify the expression.

Tap for more steps...

Step 9.1

Move the negative in front of the fraction.

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

Step 9.2

Multiply $- 1$ by $- 1$ .

$1 \frac{5 (5 - 3 \sqrt{3})}{2}$

Step 9.3

Multiply $\frac{5 (5 - 3 \sqrt{3})}{2}$ by $1$ .

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

Step 10

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.49038105 \dots$