# 12.8: Multiplication of Rational Expressions

**At Grade**Created by: CK-12

**Practice**Multiplication of Rational Expressions

### Multiplication of Rational Expressions

The rules for multiplying and dividing rational expressions are the same as the rules for multiplying and dividing rational numbers, so let’s start by reviewing multiplication and division of fractions. When we multiply two fractions we multiply the numerators and denominators separately:

**Multiplying Rational Expressions Involving Monomials**

1. Multiply the following: .

Cancel common factors from the numerator and denominator. The common factors are 4, , and . Canceling them out leaves .

2. Multiply .

Rewrite the problem as a product of two fractions: Then cancel common factors from the numerator and denominator.

The common factors are 3 and . Canceling them out leaves .

**Multiplying Rational Expressions Involving Polynomials**

When multiplying rational expressions involving polynomials, first we need to factor all polynomial expressions as much as we can. Then we follow the same procedure as before.

Multiply .

Factor all polynomial expressions as much as possible:

The common factors are and . Canceling them leaves .

**Multiplying a Rational Expression by a Polynomial**

When we multiply a rational expression by a whole number or a polynomial, we can write the whole number (or polynomial) as a fraction with denominator equal to one. We then proceed the same way as in the previous examples.

Multiply .

Rewrite the expression as a product of fractions:

Factor polynomials:

The common factor is . Canceling it leaves

### Example

#### Example 1

Multiply .

Factor polynomials: .

The common factors are and . Canceling them leaves

### Review

Multiply the following rational expressions and reduce the answer to lowest terms.

### Review (Answers)

To view the Review answers, open this PDF file and look for section 12.8.

### Notes/Highlights Having trouble? Report an issue.

Color | Highlighted Text | Notes | |
---|---|---|---|

Please Sign In to create your own Highlights / Notes | |||

Show More |

### Image Attributions

Here you'll learn how to multiply two monomial rational expressions, two polynomial rational expressions, and a rational expression by a polynomial.

## Concept Nodes:

**Save or share your relevant files like activites, homework and worksheet.**

To add resources, you must be the owner of the Modality. Click Customize to make your own copy.