1. Section 5.2 Products and Quotients of Rational Expressions
Algebra II
Section 5.2
Products and Quotients of Rational Expressions

2. Warm-up
Simplify each expression. Assume all variables are nonzero. #1 𝑥 5 ∙ 𝑥 2 #2 𝑦 3 ∙ 𝑦 3 #3 𝑥 6 𝑥 2 #4 𝑦 2 𝑦 5

3. You’re getting warmer!
Factor #5 𝑥 2 −2𝑥−8 #6 𝑥 2 −5𝑥 #7 𝑥 5 −9 𝑥 3

4. Rational Expression- quotient of two polynomials
Simplifying a rational expression means factoring and reducing.

5. NEVER,NEVER,NEVER REDUCE TERMS!!!!
You can reduce any FACTOR in the numerator with any FACTOR in the denominator.
NEVER,NEVER,NEVER REDUCE TERMS!!!!

6. #1 Never go in the dressing room
If you have more than one term in the numerator or denominator, dress the expression in parentheses.
Two rules
#1 Never go in the dressing room
#2 Never take anything out before it is
dressed!

7. Factor First, Then Reduce!!!
In a Nutshell!
Factor First, Then Reduce!!!

8. A rational expression is undefined if a value of x would make the denominator equal zero
Set a denominator equal to zero to find x-values where the expression is undefined .

9. Identify any values where the expression is undefined.
−𝑥−4 𝑥 2 −𝑥−20

10. Try these!
Page 324 #2-7

11. Vintage Math
Recall the rules for multiplying fractions!

12. Simplify fractions! Use parentheses with multi-term numerator
and/or denominator
Factor each!
Reduce like factors!
NEVER CANCEL INSIDE PARENTHESES!

13. Numerator and Denominator
Always dress them up before you take anything out!

14. When multiplying rational expressions-
#1 Factor all numerators and denominators
completely (remember parentheses)
#2 Cancel any numerator with any
denominator!
#3 Multiply what’s left-
numerator x numerator
denominator x denominator

15. Factoring check
#1 GCF?
#2 Difference of perfect squares?
#3 Factorable trinomial?
#4 Factor out a -1?

16. 5−𝑥 𝑥−5 = −1(−5+𝑥) (𝑥−5) = −1 Is the difference of two terms switched?
Factor a negative one out of the numerator or denominator
Now you can do some canceling!
5−𝑥 𝑥−5 = −1(−5+𝑥) (𝑥−5) = −1

17. Factor 1st, then reduce! #1 22 𝑧 2 15 ∙ −5 11 𝑧 3
# 𝑧 ∙ −5 11 𝑧 3
# 𝑥 2 −5𝑥+4 𝑥 5 ∙ 𝑥 3 𝑥 2 −2𝑥−8

18. Try these!
Pg #8-10

19. More vintage math
Recall rules for dividing fractions-

20. Complex fractions - a fraction divided by another fraction which can be rewritten as a division problem.
= ÷ 2 3 = 4 9 × 3 2 = 2 3

21. Factor 1st, keep, flip, then reduce!
𝑥 2 +4𝑥−12 9 𝑥 2 −4 ÷ 𝑥 2 −6𝑥+8 9𝑥−6

22. Try these!
Pg #11-14

23. If you have an equation with a fraction, simplify the fraction
If you have an equation with a fraction, simplify the fraction. Sometimes the fraction disappears!

24. Solving an equation.
Simplify the fractions in the equation!
When you get your final answer- YOU MUST CHECK IT IN THE ORIGINAL EQUATION!
Any value that results in a denominator of zero is eliminated from the solution set.

25. A possible way to eliminate fractions in an equation.
Factor and reduce the fraction so the
denominator is one

26. Extraneous roots- answers to a changed equation that do not work in the original equation.

27. Solve for x. Check answers in ORIGINAL equation.
#1 4 𝑥 2 −1 2𝑥−1 =9
#2 𝑥 2 +3𝑥−28 (𝑥+7)(𝑥−4) = 11

28. Try these!
Pg 324 #15-17

29. Homework/classwork
Pg #18-34, 47-49