A rational expression is in simplified form when the numerator and denominator have no common factors other than 1. To simplify a rational expression, factor the numerator and denominator and cancel any common factors; this works the same as multiplying fractions by multiplying numerators and denominators and then simplifying. Examples are provided for multiplying and dividing rational expressions by factoring, multiplying or dividing numerators and denominators, and then simplifying.

2.  A rational expression is in simplified
form when its numerator and
denominator have no common factors
(other than 1).
 To simplify:
1. Factor numerator and denominator.
2. Cancel any common factors.
(Common terms do not cancel!)

3.  Simplify:

4.  Simplify:

5.  Works the same as multiplying fractions:
 Multiply numerators
 Multiply denominators
 Simplify
 Example: (with Monomials Only)
 Multiply:

6.  Multiply:

7.  Factor numerators and denominators first.
 Then, multiply
(don’t FOIL, keep in factored form)
 Simplify.
 Example
 Multiply:

8.  Multiply:

9.  Writethe polynomial over 1.
 Then, multiply as before.
 Example:
Hint:

10.  Multiply:

11.  Todivide: flip and multiply.
 Then simplify.
 Example:

12.  Divide:

13.  Write the polynomial under 1.
 Then divide as before.
 Example:
 Divide:

14.  Divide:

15.  Simplify:

16.  Simplify: