4.4.1 a/b − (na − 1)/(nb − 1)

This formula deals with subtracting expressions where one fraction is derived from another.

Formula 1: When numerator and denominator are one less

$$\frac{a}{b} - \frac{na - 1}{nb - 1} = \frac{b - a}{b \cdot (nb - 1)}$$

Example

$$\frac{3}{5} - \frac{17}{29} = \frac{5 - 3}{5 \cdot 29} = \frac{2}{145}$$

Formula 2: When numerator and denominator are one more

$$\frac{a}{b} - \frac{na + 1}{nb + 1} = \frac{-(b - a)}{b \cdot (nb + 1)}$$

Tip: Look at the “complicated” fraction to determine if its numerator and denominator are one greater or one less than a multiple of the “simpler” fraction’s values.

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Problem Set 4.4.1

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