Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{5 (- 3 + 3 \sqrt{3})}{- 18}$

Step 5

Cancel the common factor of $- 3 + 3 \sqrt{3}$ and $- 18$ .

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Step 5.1

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

$\frac{3 (5 (- 1 + \sqrt{3}))}{- 18}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $- 18$ .

$\frac{3 (5 (- 1 + \sqrt{3}))}{3 (- 6)}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (5 (- 1 + \sqrt{3}))}{3 \cdot - 6}$

Step 5.2.3

Rewrite the expression.

$\frac{5 (- 1 + \sqrt{3})}{- 6}$

Step 6

Move the negative in front of the fraction.

$- \frac{5 (- 1 + \sqrt{3})}{6}$

Step 7

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

$- \frac{5 (- 1 (1) + \sqrt{3})}{6}$

Step 8

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

$- \frac{5 (- 1 (1) - 1 (- \sqrt{3}))}{6}$

Step 9

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

$- \frac{5 (- 1 (1 - \sqrt{3}))}{6}$

Step 10

Simplify the expression.

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Step 10.1

Move the negative in front of the fraction.

$- - \frac{5 (1 - \sqrt{3})}{6}$

Step 10.2

Multiply $- 1$ by $- 1$ .

$1 \frac{5 (1 - \sqrt{3})}{6}$

Step 10.3

Multiply $\frac{5 (1 - \sqrt{3})}{6}$ by $1$ .

$\frac{5 (1 - \sqrt{3})}{6}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{5 (1 - \sqrt{3})}{6}$

Decimal Form:

$- 0.61004233 \dots$