Precalculus Examples

$\frac{1}{1 - \frac{1}{3}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{1}{\frac{3}{3} - \frac{1}{3}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{\frac{3 - 1}{3}}$

Step 1.3

Subtract $1$ from $3$ .

$\frac{1}{\frac{2}{3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{3}{2})$

Step 3

Multiply $\frac{3}{2}$ by $1$ .

$\frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$