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,
 |