Multiplying Rational Expressions

Multiplying rational expressions is like multiplying fractions.

Procedure — To Multiply Rational Expressions

Step 1 Factor the numerators and denominators.

Step 2 Cancel all pairs of factors common to the numerators and denominators.

Step 3 Multiply the numerators. Multiply the denominators.

Note:

Here’s an example from arithmetic:

Multiply and write the answer in lowest terms:

Step 1 Factor the numerators and denominators.
Step 2 Cancel all pairs of factors common to the numerators and denominators.
Step 3 Multiply the numerators. Multiply the denominators.

Thus,

Example 1

Find:

Solution
Step 1 Factor the numerators and denominators.
Step 2 Cancel all pairs of factors common to the numerators and denominators.
Step 3 Multiply the numerators. Multiply the denominators.

Thus,

Notice that is in lowest terms.

Example 2

Find:

Solution
Step 1 Factor the numerators and denominators.
Step 2 Cancel all pairs of factors common to the numerators and denominators.
Step 3 Multiply the numerators. Multiply the denominators.

Thus,