1. Simplify each expression. Assume all variables are nonzero.
Warm Up
Simplify each expression. Assume all variables are nonzero.
1. x5  x2 x7
2. y3  y3 y6 3. x6 x2 4. y2 y5 1 y3 x4
Factor each expression.
5. x2 – 2x – 8
(x – 4)(x + 2)
6. x2 – 5x
x(x – 5)
7. x5 – 9x3
x3(x – 3)(x + 3)

2. This weeks required assignments for today no extension:
Algebra 1- AA1, AA2 IXL Proficiency -85%
Algebra 2- N4
TODAY- Friday 3/22
Algebra 1- Y3, Y5, V8 - 90% proficiency
Extra Credit (must have completed all of the above for Extra Credit PRIOR TO COMPLETING)
8th Grade math ( BB6, BB7) – 95% proficiency

3. Simplifying, Multiplying, and Dividing
4B.1
Simplifying, Multiplying, and Dividing
Rational Expressions
Holt McDougal Algebra 2
Holt Algebra 2

4. Objectives Simplify rational expressions.
Multiply and divide rational expressions.

5. Vocabulary
rational expression

6. A rational expression is a quotient of two polynomials
A rational expression is a quotient of two polynomials. Other examples of rational expressions include the following:

7. Steps to simplify:
Factor numerator & denominator
State excluded values
Set each factor in the denominator equal to zero and solve.
Only for simplifying
Simplify by cancelling out like factors on top and bottom.

8. SIMPLIFYING

9. Example 1A: Simplifying Rational Expressions
Simplify. Identify any x-values for which the expression is undefined.
10x8
6x4
510x8 – 4 36

10. Example 1B: Simplifying Rational Expressions
Simplify. Identify any x-values for which the expression is undefined.
x2 + x – 2
x2 + 2x – 3
Factor; then divide out common factors.
(x + 2)(x – 1)
(x – 1)(x + 3)
(x + 2)
(x + 3) =

11. You Try! Simplify. Identify any x-values for which the expression is undefined.
Example 1C Example 1D
16x11
8x2
3x + 4
3x2 + x – 4
28x11 – 2 18
(3x + 4)
(3x + 4)(x – 1) 1
(x – 1)

12. MULTIPLYING

13. Sponge
Simplify each. Then solve the denominators to find what is know as the “excluded values” (this means x cannot be this value so we exclude it).
16x11
8x2
3x + 4
3x2 + x – 4 1. 2.

14. Multiply. Assume all expressions are defined.
3x5y3
2x3y7 
10x3y4
9x2y5
x – 3
4x + 20 
x + 5
x2 – 9
1A.
1B.
x – 3
4(x + 5) 
x + 5
(x – 3)(x + 3)

15. You Try! Multiply. Assume that all expressions are defined.
Example 2b Example 2c x 15  20 x4 2x x7
10x – 40
x2 – 6x + 8 
x + 3
5x + 15

16. (then the problem becomes multiplication)
DIVIDING
STEPS
Keep
Change
Flip
(then the problem becomes multiplication)

17. Example 1A: Dividing Rational Expressions
Divide. Assume that all expressions are defined.
5x4
8x2y2 ÷
8y5 15
5x4
8x2y2  15
8y5

18. Example 1B: Dividing Rational Expressions
Divide. Assume that all expressions are defined.
x4 – 9x2
x2 – 4x + 3 ÷
x4 + 2x3 – 8x2
x2 – 16
x4 – 9x2
x2 – 4x + 3 
x2 – 16
x4 + 2x3 – 8x2
x2 (x2 – 9)
x2 – 4x + 3 
x2 – 16
x2(x2 + 2x – 8)
(x + 3)(x – 4)
(x – 1)(x – 2)

19. 2A You Try! Divide.
Example 3C Example 3D x2 4 ÷
12y2
x4y
2x2 – 7x – 4
x2 – 9 ÷
4x2– 1
8x2 – 28x +12

20. Copy each and complete. I know…. There is not a #1, nor 5-7).

21. Back of handout from last week with checks!HW

23. Week of 3-18 This weeks required IXL assignments After Classwork!
Part 1 must be completed “by the end of class” (no late work accepted).
Part 1: Algebra 1- AA1, AA2, GG3
IXL Proficiency -85%
Algebra 2- N4
Now “TODAY”- Friday 3/22
Algebra 1- Y3, Y5, V8 - 90% proficiency
Extra Credit (must have completed all of the above for Extra Credit PRIOR TO COMPLETING)
8th Grade math ( BB6, BB7) – 95% proficiency