Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} \cdot \frac{1}{1 - \frac{1}{2}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{1}{2} \cdot \frac{1}{\frac{2}{2} - \frac{1}{2}}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{1}{\frac{2 - 1}{2}}$

Step 2.3

Subtract $1$ from $2$ .

$\frac{1}{2} \cdot \frac{1}{\frac{1}{2}}$

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.

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

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $1 \cdot 2$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$1$