1. Bell Ringer
Find the points of intersection for the following functions.
𝑓 𝑥 = 𝑥 2 +2𝑥−3
𝑔 𝑥 =−2𝑥+2

2. Multiplying & Dividing Rational Expressions
December 4, 2015

3. Objective Essential Question
Today students will learn how to simplify rational expressions that are multiplied or divided.
In what ways does this concept connect to another mathematical concept?
Objective Essential Question

4. Steps for Simplifying rational functions
Factor the numerator.
Factor the denominator.
Look for any common factors. (These cancel each other out)
DO NOT TRY TO CANCEL OUT A TERM IF IT IS NOT BEING MULTIPLIED
Rewrite in simplest form.

5. 2𝑥+2 (𝑥+1)(𝑥+3)

6. 40𝑥+20 10𝑥+30

7. 𝑥 2 −2𝑥−15 𝑥 2 −9

8. 𝑥+4 𝑥 2 −16

9. Steps for Multiplication
Factor each fraction. Simplify if possible.
Multiply across the numerators.
Multiply across the denominators.
Simplify any common factors.

10. 4(𝑥+5) 𝑥 2 ∙ 𝑥(𝑥+1) 2(𝑥+5)

11. 3𝑥−12 𝑥+5 ∙ 𝑥+6 2𝑥−8

12. 𝑥+2 𝑥 3 −27 ∙ 𝑥 2 +3𝑥+9

13. Steps for dividing two rational fractions
Factor each numerator and denominator separately. Simplify anything (if possible) Copy the first fraction. Multiply by the second fraction’s reciprocal Multiply and simplify.

14. 5 𝑥 2 𝑦 3 𝑥 7 ÷ 30𝑥 𝑦 4 𝑦 3

15. (𝑥+3)(𝑥−2) 𝑥(𝑥+1) ÷ 𝑥+3 𝑥

16. 8 𝑥 2 𝑥+4 ÷ 𝑥 2(𝑥−4)

17. 𝑥 2 −6𝑥−27 2𝑥 2 +2𝑥 ÷ 𝑥+3 𝑥

18. No homework!