Dividing Rational Expressions
You probably know how to divide rational expressions containing monomials.
Now, we will use the same procedure to divide rational expressions that
contain binomials or trinomials.
Note:
Here is an example of dividing rational
expressions that contain monomials:
Procedure â€”
To Divide Rational Expressions
Step 1 Invert the second fraction and change the division symbol,
Ã·, to the multiplication symbol,
Â·.
Step 2 Factor the numerators and denominators.
Step 3 Cancel all pairs of factors common to the numerators and
denominators.
Step 4 Multiply the numerators. Multiply the denominators.
We usually leave the answer in factored form.
Example 1
Find:
Solution 

Step 1 Invert the second fraction
and change the division
symbol, Ã·, to the
multiplication symbol, Â· . 

Step 2 Factor the numerators
and denominators.


Step 3 Cancel all pairs of factors
common to the numerators
and denominators.


Step 4 Multiply the numerators.
Multiply the denominators. 

Thus,
Example 2
Find:
Solution 

Step 1 Invert the second fraction
and change the division
symbol, Ã·, to the
multiplication symbol, Â·. 

Step 2 Factor the numerators and
denominators.


Step 3 Cancel all pairs of factors
common to the numerators and denominators. 

Replace
with
1. 

Step 4 Multiply the numerators.
Multiply the denominators. 

Thus,
Note:
You can also write the answer as follows:
