Precalculus Examples

$\frac{2 (\frac{1}{6})}{1 - {(\frac{1}{6})}^{2}}$

Step 1

Combine $2$ and $\frac{1}{6}$ .

$\frac{\frac{2}{6}}{1 - {(\frac{1}{6})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $\frac{1}{6}$ .

$\frac{\frac{2}{6}}{1 - \frac{1^{2}}{6^{2}}}$

Step 2.2

One to any power is one.

$\frac{\frac{2}{6}}{1 - \frac{1}{6^{2}}}$

Step 2.3

Raise $6$ to the power of $2$ .

$\frac{\frac{2}{6}}{1 - \frac{1}{36}}$

Step 2.4

Write $1$ as a fraction with a common denominator.

$\frac{\frac{2}{6}}{\frac{36}{36} - \frac{1}{36}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{\frac{2}{6}}{\frac{36 - 1}{36}}$

Step 2.6

Subtract $1$ from $36$ .

$\frac{\frac{2}{6}}{\frac{35}{36}}$

Step 3

Cancel the common factor of $2$ and $6$ .

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Step 3.1

Factor $2$ out of $2$ .

$\frac{\frac{2 (1)}{6}}{\frac{35}{36}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6$ .

$\frac{\frac{2 \cdot 1}{2 \cdot 3}}{\frac{35}{36}}$

Step 3.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 1}{2 \cdot 3}}{\frac{35}{36}}$

Step 3.2.3

Rewrite the expression.

$\frac{\frac{1}{3}}{\frac{35}{36}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{3} \cdot \frac{36}{35}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $36$ .

$\frac{1}{3} \cdot \frac{3 (12)}{35}$

Step 5.2

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3 \cdot 12}{35}$

Step 5.3

Rewrite the expression.

$\frac{12}{35}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{12}{35}$

Decimal Form:

$0.3\overline{428571}$