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. |
![](./articles_imgs/775/multip2.gif) |
Step 2 Cancel all pairs of factors common
to the numerators and
denominators.
|
![](./articles_imgs/775/multip3.gif) |
Step 3 Multiply the numerators.
Multiply the denominators. |
![](./articles_imgs/775/multip4.gif) |
Thus,
![](./articles_imgs/775/multip5.gif)
Example 1
Find:
![](./articles_imgs/775/multip6.gif)
Solution |
![](./articles_imgs/775/multip7.gif) |
Step 1 Factor the numerators and
denominators.
|
![](./articles_imgs/775/multip8.gif) |
Step 2 Cancel all pairs of factors
common to the numerators
and denominators.
|
![](./articles_imgs/775/multip9.gif) |
Step 3 Multiply the numerators.
Multiply the denominators. |
![](./articles_imgs/775/multip10.gif) |
Thus,
![](./articles_imgs/775/multip11.gif)
Notice that
is in lowest terms.
Example 2
Find:
![](./articles_imgs/775/multip13.gif)
Solution |
![](./articles_imgs/775/multip14.gif) |
Step 1 Factor the numerators and
denominators.
|
![](./articles_imgs/775/multip15.gif) |
Step 2 Cancel all pairs of factors
common to the numerators
and denominators.
|
![](./articles_imgs/775/multip16.gif) |
Step 3 Multiply the numerators.
Multiply the denominators. |
![](./articles_imgs/775/multip17.gif) |
Thus,
![](./articles_imgs/775/multip18.gif) |