1. 9.4 Multiplying & Dividing Rational Expressions

2. Simplifying Rational Expressions
If the top and bottom have a common term, they can cancel out.

3. Example #1 Simplify the Expression
Do you notice anything similar on top and bottom?

4. Example #1b Simplify the Expression
Notice how the top and bottom both have “(x – 2)”. They cancel out.
Also, notice the top has “(x + 3)” and the bottom has “(x – 3),” which are different. They DO NOT cancel out.

5. Example #1c Simplify the Expression
Notice “x2 – 4” can be factored to (x + 2)(x – 2)
Notice how the top and bottom both have “(x – 2)”. They cancel out.
Again, the top has “(x + 2)” and the bottom has “(x – 3),” so they DO NOT cancel out.

6. Example #2a Multiply How do you multiply fractions? Straight across
We don’t even want to multiply, we just want to cancel.
Is there anything we can cancel?

7. Example #2b Multiply 2 How do you multiply fractions? Straight across
We don’t even want to multiply, we just want to factor, then cancel.

8. Example #3a Divide
Dividing is the same as multiplying by the reciprocal.
Again, we don’t even want to multiply.

9. Example #3b Divide 3 3 3 = 2 3 2
Dividing is the same as multiplying by the reciprocal.
Again, we don’t even want to multiply.

10. Simplify the expression
Practice #1
Simplify the expression

11. Simplify the expression
Practice #2
Simplify the expression

12. Practice #3
Multiply or

13. Practice #4
Divide

14. Practice #5
Divide