1. Multiplying and Dividing Rational Expressions
5.2
Multiplying and Dividing Rational Expressions

2. Multiplying Rational Expressions
If are rational expressions, then
To multiply rational expressions, multiply the numerators and then multiply the denominators.

3. Multiplying Rational Expressions
After multiplying such expressions, our result may not be in simplified form, so we use the following techniques.
To Multiply Rational Expressions
Step 1: Completely factor numerators and denominators.
Step 2: Multiply numerators and multiply denominators.
Step 3: Simplify or write the product in lowest terms by dividing out common factors.

4. Multiplying Rational Expressions
Example
6x2 5x
Multiply: •
10x3 12

5. Multiplying Rational Expressions
Example
(m – n)2 m
Multiply: •
m + n
m 2 – mn

6. Dividing Rational Expressions
If are rational expressions, then
To divide two rational expressions, multiply the first rational expression by the reciprocal of the second rational expression.

7. Helpful Hint
Remember, to Divide by a Rational Expression, multiply by its reciprocal.

8. Dividing Rational Expressions
Example
Divide:

9. Units of Measure Converting Between Units of Measure
Use unit fractions (equivalent to 1), but with different measurements in the numerator and denominator.
Multiply the unit fractions like rational expressions, canceling common units in the numerators and denominators.

10. Units of Measure 1008 square inches = _________ square feet.
Example
1008 square inches = _________ square feet.
(1008 sq in)
(2·2·2·2·3·3·7 in · in)