Lesson 3.3

Multiplying Rational Expressions

Multiplying rational expressions follows the same rule as numeric fractions: multiply straight across, then simplify.

Introduction

Remember: . Rational expressions work the same way — but we always factor first so we can cancel before multiplying.

Past Knowledge

Factoring (Unit 2) and simplifying rational expressions (Lesson 3.2).

Today's Goal

Factor, cancel common factors across numerators and denominators, then multiply.

Future Success

This same process extends to dividing rational expressions in the next lesson.

Key Concepts

The Rule

Multiply numerator × numerator, denominator × denominator.

💡 Pro tip: Factor and cancel first — it's much easier than expanding and then trying to simplify.

Step-by-Step

1

Factor all numerators and denominators

2

Cancel any factor that appears in a numerator AND a denominator

3

Multiply remaining factors across

Worked Examples

Example 1: Monomial × Binomial

Basic

Multiply .

1

Cancel

2

Simplify

Example 2: Trinomial Factors

Intermediate

Multiply .

1

Factor everything

2

Cancel , , and

Example 3: Three Expressions

Advanced

Multiply .

1

Factor

2

Cancel , , and one

Common Pitfalls

Multiplying Before Factoring

If you multiply first, you get a much harder expression to simplify. Always factor first.

Cross-Cancelling Incorrectly

You can cancel a factor from any numerator with any denominator — but only if they're the same factor.

Real-Life Applications

Unit conversions in science are chains of multiplied fractions. Converting 60 miles/hour to feet/second requires multiplying three rational expressions — and cancelling units works exactly like cancelling polynomial factors.

Practice Quiz

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