Multiply Rational Expressions Calculator
Multiply rational expressions with factoring, cross-cancellation, and step-by-step solutions
First Rational Expression
Second Rational Expression
How to Multiply Rational Expressions
Method Overview
Multiplying rational expressions is similar to multiplying numerical fractions, but we factor and simplify first to make the work easier.
Step 1: Factor All Expressions
Factor each numerator and denominator completely before multiplying.
Step 2: Cross-Cancel Common Factors
Cancel factors that appear in any numerator with the same factors in any denominator. This is much easier than multiplying first then simplifying!
Step 3: Multiply Remaining Factors
Multiply the remaining factors in the numerators together and the remaining factors in the denominators together.
Step 4: State Restrictions
Include all values that make any original denominator equal to zero.
Example
Multiply: (x² - 4)/(x + 3) × (x + 3)/(x + 2)
- Factor: [(x+2)(x-2)]/(x+3) × (x+3)/(x+2)
- Cancel (x+3) and (x+2)
- Result: x - 2, where x ≠ -3, -2
Frequently Asked Questions
Why factor before multiplying?
Factoring first allows you to cross-cancel common factors before multiplying, resulting in simpler expressions and less work overall.
Can I cancel factors diagonally?
Yes! You can cancel any factor from any numerator with the same factor from any denominator. This is called cross-cancellation.
What if nothing cancels?
If there are no common factors after factoring, simply multiply all numerators together and all denominators together. The result may be factorable afterward.
Do I need to multiply out the final answer?
Generally, no. Leave the answer in factored form unless specifically asked to expand it. Factored form is usually considered simplest.
How do I find all restrictions?
Set each original denominator equal to zero and solve. The solutions are the restricted values. Don't forget any denominators that were canceled!
Can I cancel before factoring?
No! You must factor completely first. You can only cancel factors, not terms. For example, you cannot cancel x from (x+2)/x.
What if a numerator and denominator are identical?
If an entire numerator and denominator are the same, they cancel to 1. But remember the restriction from that denominator!
Is multiplication of rational expressions commutative?
Yes! The order doesn't matter: (a/b)(c/d) = (c/d)(a/b). However, factoring and canceling might look different depending on your approach.