Precalculus Examples

$\frac{\frac{1}{14}}{\frac{1}{6} - \frac{1}{7}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{14} \cdot \frac{1}{\frac{1}{6} - \frac{1}{7}}$

Step 2

Simplify the denominator.

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Step 2.1

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{14} \cdot \frac{1}{\frac{1}{6} \cdot \frac{7}{7} - \frac{1}{7}}$

Step 2.2

To write $- \frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{1}{14} \cdot \frac{1}{\frac{1}{6} \cdot \frac{7}{7} - \frac{1}{7} \cdot \frac{6}{6}}$

Step 2.3

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{1}{6}$ by $\frac{7}{7}$ .

$\frac{1}{14} \cdot \frac{1}{\frac{7}{6 \cdot 7} - \frac{1}{7} \cdot \frac{6}{6}}$

Step 2.3.2

Multiply $6$ by $7$ .

$\frac{1}{14} \cdot \frac{1}{\frac{7}{42} - \frac{1}{7} \cdot \frac{6}{6}}$

Step 2.3.3

Multiply $\frac{1}{7}$ by $\frac{6}{6}$ .

$\frac{1}{14} \cdot \frac{1}{\frac{7}{42} - \frac{6}{7 \cdot 6}}$

Step 2.3.4

Multiply $7$ by $6$ .

$\frac{1}{14} \cdot \frac{1}{\frac{7}{42} - \frac{6}{42}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{1}{14} \cdot \frac{1}{\frac{7 - 6}{42}}$

Step 2.5

Subtract $6$ from $7$ .

$\frac{1}{14} \cdot \frac{1}{\frac{1}{42}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{14} (1 \cdot 42)$

Step 3.2

Multiply $42$ by $1$ .

$\frac{1}{14} \cdot 42$

Step 3.3

Cancel the common factor of $14$ .

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Step 3.3.1

Factor $14$ out of $42$ .

$\frac{1}{14} \cdot (14 (3))$

Step 3.3.2

Cancel the common factor.

$\frac{1}{14} \cdot (14 \cdot 3)$

Step 3.3.3

Rewrite the expression.

$3$