Multiply Rational Expressions

Multiply Rational Expressions

When multiplying rational expressions, treat them like fractions with variables.

1) Factor first

Before multiplying, factor every polynomial in the numerators and denominators as much as possible. This makes it easier to see common factors.

2) Multiply straight across

After factoring, multiply the numerators together and the denominators together:

• numerator × numerator
• denominator × denominator

3) Cancel common factors

If the same factor appears in both a numerator and a denominator, cancel it. Only factors can be canceled, not terms added by + or −.

4) Simplify the result

Write the product in simplest form. If the answer can be reduced further, do so.

5) Check for restrictions

Any value that makes an original denominator zero is not allowed. Even if a factor cancels, those values are still excluded from the domain.

Quick check

Your final answer should be simplified, with no common factors left between numerator and denominator. Also verify that the original denominators are never zero.

A good habit is to factor first, cancel second, and multiply what remains. This helps avoid errors and keeps the expression as simple as possible.