Calculus Examples

$\frac{a}{b} - \frac{c}{d}$

Step 1

To write $\frac{a}{b}$ as a fraction with a common denominator, multiply by $\frac{d}{d}$ .

$\frac{a}{b} \cdot \frac{d}{d} - \frac{c}{d}$

Step 2

To write $- \frac{c}{d}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{a}{b} \cdot \frac{d}{d} - \frac{c}{d} \cdot \frac{b}{b}$

Step 3

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

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Step 3.1

Multiply $\frac{a}{b}$ by $\frac{d}{d}$ .

$\frac{a d}{b d} - \frac{c}{d} \cdot \frac{b}{b}$

Step 3.2

Multiply $\frac{c}{d}$ by $\frac{b}{b}$ .

$\frac{a d}{b d} - \frac{c b}{d b}$

Step 3.3

Reorder the factors of $d b$ .

$\frac{a d}{b d} - \frac{c b}{b d}$

Step 4

Combine the numerators over the common denominator.

$\frac{a d - c b}{b d}$