Chapter 9
“Rational Functions and Relations”
Date
Section
Topic
01/19
9.1
Multiplying Rational Expressions
01/20
9.1
Dividing Rational Expressions
P. 558: 20, 22, 28, 30, 34, 43, 44, 48
01/21
9.1
Dividing Rational Expressions
P. 558: 35-38, 49, 51
P. 566: 36-38
01/22
9.1
Dividing Rational Expressions
Worksheet #4
01/25
QUIZ (9.1)
01/26
9.2
01/27
9.2
01/28
9.6
Adding and Subtracting Rational
Expressions
Adding and Subtracted Rational
Expressions
Rational Equations
Assignment
P. 558: 17, 21, 23, 25, 33, 42, 45
TBD
P. 565: 5, 7, 9, 11, 23, 28
P. 565: 25, 29, 31, 36, 37, 45, 70
P. 600: 1, 5, 18, 20
01/29
Applications of Rational Equations
Worksheet #9
02/01
QUIZ (9.1–9.6)
Review Packet
02/02
REVIEW
02/03
CHAPTER 9 TEST
Advanced Algebra w/ Trig
Notes 9.1 – Day 1
Multiplying Rational Expressions
Goal: Students will be able to multiply rational expressions.
Steps to Simplify:
1. Get rid of negative exponents (if needed)
2. Factor
a. GCF
b. (
)(
)
3. Cancel Like Terms
4. Simplify Coefficients
Simplify.
x 2  5x  24
1.
2x 2  6x
3.
15  3a
a 2  25
5.
7a
9b
63b3
35a 2
y 3  ay 2
2.
y 2  ay
4.
z2w  z2
z3  z3w
6.
6rst 2
5s 2 t
4r 2 s
3st 2
7.
3x 2  5 x  28
x 2  3x  28
x2
9.
x3
x2  8x  7
3x  7
 x 2  x  12 


2
 x 9 
8.
5 x
10 x  2
10.
x3  1
1  x2
1
25 x 2  1
x 2  10 x  25
x2  2x 1
x2  x  1
Advanced Algebra w/ Trig
Notes 9.1 – Day 2
Dividing Rational Expressions
Goal: Students will be able to divide rational expressions.
Steps to Simplify:
1. Get rid of negative exponents (if needed)
2. Flip term behind the 
3. Factor
a. GCF
b. (
)(
)
4. Cancel Like Terms
5. Simplify Coefficients
Simplify.
1.
4x2 y
2 xy 2

15a 3b3 5ab3
2.
18x 2 24x

10y 2 15y3
3.
y 5
y2  4 y  5

y2  4 y  5
y 1
4.
x2  2x  3
9  x2

4x2  9
2 x2  x  3
5.
9  a2
2a  6

2
a  5a  6 5a  10
6.
c 2  6c  16 8c  c 2

c2  d 2
cd
Advanced Algebra w/ Trig
Notes 9.1 – Day 3
Dividing Rational Expressions
Goal: Students will be able to simplify complex fractions.
Steps to Simplify:
1. Factor all factions
2. Find the least common denominator for all baby fractions
3. Multiply every term by the LCD
4. Simplify
Simplify.
3 x
5
1.
4 x
10
1 1

x y
2.
1
1
x
1
x
3.
1
x
x
1 3

2
x
4.
x3
4
x
x2
x 2  25 y 2
5.
x
5y  x
x 1
2
6. 2 x  9
x  3x  4
x 2  3x
6a
a4
7.
a 2  7a
a 2  11a  28
2
3x
 2
8. x  3 x  9
3
4x
 2
x 3 x 9
Advanced Algebra w/ Trig
Notes 9.2 – Day 1
Adding & Subtracting Rational Functions
Goal: Students will be able to add and subtract rational expressions.
What is a Least Common Multiple?
Find the LCM of each set of polynomials.
1. 15a 2bc3 , 16b5c 2 , and 20a 3c 6
2. x3  x 2  2 x and x 2  4 x  4
Steps to Simplify:
1. Factor each term
2. Find the LCD (least common denominator)
3. Convert each term to have the LCD as the denominator
4. Add/Subtract numerators
5. Simplify each expression
Simplify.
3.
5a  3c a  c

2a
2a
4.
2y
3

5 x 20 y
5.
7x
4y
 2 3
2
18 xy 6 x y
6.
x  12
x4

4 x  16 2 x  8
7.
x  2 x 3

x 1 x 1
8.
9.
1
1 a

4a  4a  1 1  2 a
10.
2
3y 1
1
 2
2 y  10 y  2 y  15
8
3b
 2
2a  2b a  b 2
Advanced Algebra w/ Trig
Notes 9.6 – Day 1
Solving Rational Equations
Goal: Students will be able to solve rational equations.
Steps to solving rational equations:
1. Factor all – Simplify if possible.
2. Find LCD
3. Multiply every term by LCD - This will make all fractions go away!!
Solve.
1.
9
3
3


28 x  2 4
x2  5 x2  x  2
3. x  2

x 1
x 1
2.
6
3
7


7 x4 8
4.
x
x2 x3


x2 x2 x2
5.
3
4
1


4x x  3 x
6.
1
2
3


2
x  4 16  x
x4
Advanced Algebra w/ Trig
Notes 9.6 – Day 2
Solving Rational Expressions
Goal: Students will be able to solve applications of rational expressions.
1. Jake is a bricklayer. He can do a job in 5 days. Nick is also a bricklayer and he can do the same job that Jake did
in 4 days. How long will it take them to do the job together?
2. Gayle and Chris are painting a room. It takes them 6 hours together. If it takes Gayle 8 hours alone, how long
does it take Chris alone?
3. Two pipes fill a tank, and a different pipe drains the tank. If it takes pipe one 27 minutes to fill the tank alone
and pipe two 54 minutes to fill the tank alone, and pipe 3 drains the tank in 36 minutes, then how long will it
take to fill the tank if all three pipes are open at once?
4. The ratio of 3 more than a number to 15 more than the same number is 2 to 3. Find the number.