1. Divide Rational Expressions
29. Simplify, Multiply and
Divide Rational Expressions

2. SIMPLIFY: We have done this already when we were graphing! STEPS:
1. factor the _____________ and _______________
2. cancel out the factors that are the same in the numerator and denominator.

3. Example
Simplify

4. Example

5. MULTIPLICATION:
Factor, Simplify,
Multiply Across
Simplify AGAIN

6. Example
Simplify 2

7. Example x2 + 4x -12 x2 + 11x + 30 x2 - 2x - 35 x + 4  Simplify= 
(x + 6)(x + 5)
x + 4 =
(x – 2)(x – 7)
(x + 4)

8. when dividing by a fraction...you are really
DIVIDE:
when dividing by a fraction...you are really
___________ by the ___________

9. Factor each polynomial.
Example
x2 + 5x + 4
x2 + 4x + 3
x2 + 3x – 4
x2 + 3x 
x2 + 5x + 4
x2 + 3x 
x2 + 4x + 3
x2 + 3x – 4
(x + 1)(x + 4)
x(x + 3) x
x – 1 =
Factor each polynomial. 
(x + 3)(x + 1)
(x + 4)(x – 1)