Algebra Examples

$\frac{6}{2 + 2 \sqrt{5}}$

Step 1

Cancel the common factor of $6$ and $2 + 2 \sqrt{5}$ .

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Step 1.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 3}{2 + 2 \sqrt{5}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

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

Step 1.2.2

Factor $2$ out of $2 \sqrt{5}$ .

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

Step 1.2.3

Factor $2$ out of $2 (1) + 2 (\sqrt{5})$ .

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

Step 1.2.4

Cancel the common factor.

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

Step 1.2.5

Rewrite the expression.

$\frac{3}{1 + \sqrt{5}}$

Step 2

Multiply $\frac{3}{1 + \sqrt{5}}$ by $\frac{1 - \sqrt{5}}{1 - \sqrt{5}}$ .

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

Step 3

Multiply $\frac{3}{1 + \sqrt{5}}$ by $\frac{1 - \sqrt{5}}{1 - \sqrt{5}}$ .

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

Step 4

Expand the denominator using the FOIL method.

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

Step 5

Simplify.

$\frac{3 (1 - \sqrt{5})}{- 4}$

Step 6

Move the negative in front of the fraction.

$- \frac{3 (1 - \sqrt{5})}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 (1 - \sqrt{5})}{4}$

Decimal Form:

$0.92705098 \dots$