Algebra Examples

$\frac{5}{6 a b} - \frac{7}{8 a}$

Step 1

To write $\frac{5}{6 a b}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5}{6 a b} \cdot \frac{4}{4} - \frac{7}{8 a}$

Step 2

To write $- \frac{7}{8 a}$ as a fraction with a common denominator, multiply by $\frac{3 b}{3 b}$ .

$\frac{5}{6 a b} \cdot \frac{4}{4} - \frac{7}{8 a} \cdot \frac{3 b}{3 b}$

Step 3

Write each expression with a common denominator of $24 a b$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{6 a b}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 4}{6 a b \cdot 4} - \frac{7}{8 a} \cdot \frac{3 b}{3 b}$

Step 3.2

Multiply $4$ by $6$ .

$\frac{5 \cdot 4}{24 a b} - \frac{7}{8 a} \cdot \frac{3 b}{3 b}$

Step 3.3

Multiply $\frac{7}{8 a}$ by $\frac{3 b}{3 b}$ .

$\frac{5 \cdot 4}{24 a b} - \frac{7 (3 b)}{8 a (3 b)}$

Step 3.4

Multiply $3$ by $8$ .

$\frac{5 \cdot 4}{24 a b} - \frac{7 (3 b)}{24 a b}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 - 7 (3 b)}{24 a b}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $4$ .

$\frac{20 - 7 \cdot 3 b}{24 a b}$

Step 5.2

Multiply $- 7$ by $3$ .

$\frac{20 - 21 b}{24 a b}$