Pre-Algebra 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

Apply the distributive property.

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

Step 8

Multiply $7$ by $1$ .

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

Step 9

Multiply $- 1$ by $7$ .

$- \frac{7 - 7 \sqrt{3}}{4}$

Step 10

Split the fraction $\frac{7 - 7 \sqrt{3}}{4}$ into two fractions.

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

Step 11

Move the negative in front of the fraction.

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

Step 12

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.28108891 \dots$