Basic Math Examples

$1 - \frac{1}{1 - \frac{1}{b}}$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify the denominator.

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Step 1.1.1.1

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

$1 - \frac{1}{\frac{b}{b} - \frac{1}{b}}$

Step 1.1.1.2

Combine the numerators over the common denominator.

$1 - \frac{1}{\frac{b - 1}{b}}$

Step 1.1.2

Multiply the numerator by the reciprocal of the denominator.

$1 - (1 \frac{b}{b - 1})$

Step 1.1.3

Multiply $\frac{b}{b - 1}$ by $1$ .

$1 - \frac{b}{b - 1}$

Step 1.2

Combine into one fraction.

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Step 1.2.1

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

$\frac{b - 1}{b - 1} - \frac{b}{b - 1}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{b - 1 - b}{b - 1}$

Step 2

Simplify the numerator.

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Step 2.1

Subtract $b$ from $b$ .

$\frac{0 - 1}{b - 1}$

Step 2.2

Subtract $1$ from $0$ .

$\frac{- 1}{b - 1}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{b - 1}$