1. Multiplying and Dividing Expressions
Section 11.1
© 2012,

2. 8.4: Multiply and Divide Rational Expressions
Quick Review
Factor x2 + 6x + 9
Factor x2 – 9
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8.4: Multiply and Divide Rational Expressions

3. Rules of Simplifying Expressions
Take GCF of numerator(s) and denominator(s) if possible.
Factor the numerator(s) (top) into simplest form
Factor the denominator(s) (bottom) into the simplest form
Cancel [bottom or cross] out the factors if needed, multiply and simplify. Apply the GCF to the factors, then…
FACTOR,
CANCEL,
QUIT.
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8.4: Multiply and Divide Rational Expressions

4. 8.4: Multiply and Divide Rational Expressions
Example 1
Simplify
Don’t do this way!!
NO!
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8.4: Multiply and Divide Rational Expressions

5. 8.4: Multiply and Divide Rational Expressions
Example 1
Simplify
Step 1: Is there a GCF?
Step 2: Factor the numerator (s)
Step 3: Factor the denominator(s)
Step 4: Cancel out the factors if needed and then multiply. No
(x + 3) (x + 3)
(x + 3) (x – 3)
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8.4: Multiply and Divide Rational Expressions

6. 8.4: Multiply and Divide Rational Expressions
Example 2
Simplify
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8.4: Multiply and Divide Rational Expressions

7. 8.4: Multiply and Divide Rational Expressions
Your Turn
Simplify
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8.4: Multiply and Divide Rational Expressions

8. 8.4: Multiply and Divide Rational Expressions
Example 3
Simplify
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8.4: Multiply and Divide Rational Expressions

9. 8.4: Multiply and Divide Rational Expressions
Your Turn
Simplify
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8.4: Multiply and Divide Rational Expressions

10. Rules of Multiplying Expressions
Take GCF of numerator(s) and denominator(s) if possible.
Factor the numerator(s) (top) into simplest form
Factor the denominator(s) (bottom) into the simplest form
Cancel [bottom or cross] out the factors if needed, multiply and simplify. Apply the GCF to the factors, then…
FACTOR,
CANCEL,
QUIT.
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8.4: Multiply and Divide Rational Expressions

11. 8.4: Multiply and Divide Rational Expressions
Rational Functions
Add
Subtract
Common
Denominator
Multiply
Divide
Cancel
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8.4: Multiply and Divide Rational Expressions

12. 8.4: Multiply and Divide Rational Expressions
Example 4
Simplify
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8.4: Multiply and Divide Rational Expressions

13. 8.4: Multiply and Divide Rational Expressions
Example 5
Simplify
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8.4: Multiply and Divide Rational Expressions

14. 8.4: Multiply and Divide Rational Expressions
Your Turn
Simplify
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8.4: Multiply and Divide Rational Expressions

15. 8.4: Multiply and Divide Rational Expressions
Example 6
Simplify
Step 1: Is there a GCF?
Step 2: Factor the numerator(s) (top) into simplest form
Step 3: Factor the denominator(s) (bottom) into the simplest form
Step 4: Cancel out the factors if needed, multiply and simplify.
YES
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8.4: Multiply and Divide Rational Expressions

16. 8.4: Multiply and Divide Rational Expressions
Example 7
Simplify
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8.4: Multiply and Divide Rational Expressions

17. 8.4: Multiply and Divide Rational Expressions
Your Turn
Simplify
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8.4: Multiply and Divide Rational Expressions

18. 8.4: Multiply and Divide Rational Expressions
Example 8
Simplify
Step 1: Is there a GCF?
Step 2: Factor the numerator(s) (top) into simplest form
Step 3: Factor the denominator(s) (bottom) into the simplest form
Step 4: Cancel out the factors if needed, multiply and simplify. NO
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8.4: Multiply and Divide Rational Expressions

19. 8.4: Multiply and Divide Rational Expressions
Example 9
Simplify
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8.4: Multiply and Divide Rational Expressions

20. 8.4: Multiply and Divide Rational Expressions
Your Turn
Simplify
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8.4: Multiply and Divide Rational Expressions

21. Rules of Divide Expressions
Take GCF of numerator(s) and denominator(s) if possible.
Take the reciprocal (flip) of the second fraction. -- KEEP IT, CHANGE IT, FLIP IT --
Factor the numerator(s) (top) into simplest form
Factor the denominator(s) (bottom) into the simplest form
Cancel out the factors and cancel if needed, multiply and simplify.
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8.4: Multiply and Divide Rational Expressions

22. 8.4: Multiply and Divide Rational Expressions
Example 10
Simplify
YES
Step 1: Is there a GCF?
Step 2: Take the reciprocal (flip) of the second fraction.
Step 3: Factor the numerator(s) (top) into simplest form
Step 4: Factor the denominator(s) (bottom) into
the simplest form
Step 5: Cancel out the factors if needed, multiply and simplify.
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8.4: Multiply and Divide Rational Expressions

23. 8.4: Multiply and Divide Rational Expressions
Example 11
Simplify
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8.4: Multiply and Divide Rational Expressions

24. 8.4: Multiply and Divide Rational Expressions
Example 12
Simplify
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8.4: Multiply and Divide Rational Expressions

25. 8.4: Multiply and Divide Rational Expressions
Your Turn
Simplify
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8.4: Multiply and Divide Rational Expressions

26. 8.4: Multiply and Divide Rational Expressions
Assignment
Pg all, 7-43 odd (omit 23)
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8.4: Multiply and Divide Rational Expressions