Algebra Examples

$f (\frac{1}{12}) = \frac{1}{6 (\frac{1}{12}) - 3}$

Step 1

Simplify the denominator.

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Step 1.1

Cancel the common factor of $6$ .

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Step 1.1.1

Factor $6$ out of $12$ .

$f (\frac{1}{12}) = \frac{1}{6 (\frac{1}{6 (2)}) - 3}$

Step 1.1.2

Cancel the common factor.

$f (\frac{1}{12}) = \frac{1}{6 (\frac{1}{6 \cdot 2}) - 3}$

Step 1.1.3

Rewrite the expression.

$f (\frac{1}{12}) = \frac{1}{\frac{1}{2} - 3}$

Step 1.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$f (\frac{1}{12}) = \frac{1}{\frac{1}{2} - 3 \cdot \frac{2}{2}}$

Step 1.3

Combine $- 3$ and $\frac{2}{2}$ .

$f (\frac{1}{12}) = \frac{1}{\frac{1}{2} + \frac{- 3 \cdot 2}{2}}$

Step 1.4

Combine the numerators over the common denominator.

$f (\frac{1}{12}) = \frac{1}{\frac{1 - 3 \cdot 2}{2}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 3$ by $2$ .

$f (\frac{1}{12}) = \frac{1}{\frac{1 - 6}{2}}$

Step 1.5.2

Subtract $6$ from $1$ .

$f (\frac{1}{12}) = \frac{1}{\frac{- 5}{2}}$

Step 1.6

Move the negative in front of the fraction.

$f (\frac{1}{12}) = \frac{1}{- \frac{5}{2}}$

Step 2

Cancel the common factor of $1$ and $- 1$ .

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Step 2.1

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

$f (\frac{1}{12}) = \frac{- 1 \cdot - 1}{- \frac{5}{2}}$

Step 2.2

Move the negative in front of the fraction.

$f (\frac{1}{12}) = - \frac{1}{\frac{5}{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{1}{12}) = - (1 (\frac{2}{5}))$

Step 4

Multiply $\frac{2}{5}$ by $1$ .

$f (\frac{1}{12}) = - \frac{2}{5}$