Algebra Examples

$12 - \frac{1}{a} - \frac{1}{b}$

Step 1

To write $12$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{12 a}{a} - \frac{1}{a} - \frac{1}{b}$

Step 2

Combine the numerators over the common denominator.

$\frac{12 a - 1}{a} - \frac{1}{b}$

Step 3

To write $\frac{12 a - 1}{a}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{12 a - 1}{a} \cdot \frac{b}{b} - \frac{1}{b}$

Step 4

To write $- \frac{1}{b}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{12 a - 1}{a} \cdot \frac{b}{b} - \frac{1}{b} \cdot \frac{a}{a}$

Step 5

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

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Step 5.1

Multiply $\frac{12 a - 1}{a}$ by $\frac{b}{b}$ .

$\frac{(12 a - 1) b}{a b} - \frac{1}{b} \cdot \frac{a}{a}$

Step 5.2

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

$\frac{(12 a - 1) b}{a b} - \frac{a}{b a}$

Step 5.3

Reorder the factors of $b a$ .

$\frac{(12 a - 1) b}{a b} - \frac{a}{a b}$

Step 6

Combine the numerators over the common denominator.

$\frac{(12 a - 1) b - a}{a b}$

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

$\frac{12 a b - 1 b - a}{a b}$

Step 7.2

Rewrite $- 1 b$ as $- b$ .

$\frac{12 a b - b - a}{a b}$