Precalculus Examples

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a b}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{1}{a} + \frac{1}{b}) (a b)$

Step 2

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

$(\frac{1}{a} \cdot \frac{b}{b} + \frac{1}{b}) (a b)$

Step 3

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

$(\frac{1}{a} \cdot \frac{b}{b} + \frac{1}{b} \cdot \frac{a}{a}) (a b)$

Step 4

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

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Step 4.1

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

$(\frac{b}{a b} + \frac{1}{b} \cdot \frac{a}{a}) (a b)$

Step 4.2

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

$(\frac{b}{a b} + \frac{a}{b a}) (a b)$

Step 4.3

Reorder the factors of $b a$ .

$(\frac{b}{a b} + \frac{a}{a b}) (a b)$

Step 5

Combine the numerators over the common denominator.

$\frac{b + a}{a b} (a b)$

Step 6

Cancel the common factor of $a b$ .

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Step 6.1

Cancel the common factor.

$\frac{b + a}{a b} (a b)$

Step 6.2

Rewrite the expression.

$b + a$