Finite Math Examples

$\frac{7}{2 - 2 \sqrt{3}}$

Step 1

Multiply $\frac{7}{2 - 2 \sqrt{3}}$ by $\frac{2 + 2 \sqrt{3}}{2 + 2 \sqrt{3}}$ .

$\frac{7}{2 - 2 \sqrt{3}} \cdot \frac{2 + 2 \sqrt{3}}{2 + 2 \sqrt{3}}$

Step 2

Multiply $\frac{7}{2 - 2 \sqrt{3}}$ by $\frac{2 + 2 \sqrt{3}}{2 + 2 \sqrt{3}}$ .

$\frac{7 (2 + 2 \sqrt{3})}{(2 - 2 \sqrt{3}) (2 + 2 \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 (2 + 2 \sqrt{3})}{4 + 4 \sqrt{3} - 4 \sqrt{3} - 4 {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{7 (2 + 2 \sqrt{3})}{- 8}$

Step 5

Cancel the common factor of $2 + 2 \sqrt{3}$ and $- 8$ .

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Step 5.1

Factor $2$ out of $7 (2 + 2 \sqrt{3})$ .

$\frac{2 (7 (1 + \sqrt{3}))}{- 8}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $- 8$ .

$\frac{2 (7 (1 + \sqrt{3}))}{2 (- 4)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (7 (1 + \sqrt{3}))}{2 \cdot - 4}$

Step 5.2.3

Rewrite the expression.

$\frac{7 (1 + \sqrt{3})}{- 4}$

Step 6

Move the negative in front of the fraction.

$- \frac{7 (1 + \sqrt{3})}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 (1 + \sqrt{3})}{4}$

Decimal Form:

$- 4.78108891 \dots$