Algebra
Chapter 12
Rational Expressions
1
Table of Contents
Day 1: Undefined &Simplifying Rational Expressions ………………….…………………………Page 3
HW: Pages 8 – 9 in Packet
Day 2: Multiplying and Dividing Rational Expressions ……………………………..……………… Page 10
HW: Pages 17 – 18 in Packet
Day 3: Review of Dividing Rational Expressions ……………………………….…..…………… Page 19
HW: Pages 19 – 22 in Packet
Day 4: QUIZ
Day 4: Adding & Subtracting Rational Expressions (Same Denominators) …………………….……Page 23
HW: Page 27 in Packet
Day 5: Adding & Subtracting Rational Expressions (Unlike Denominators) …………………….… Page 28
HW: Page 33 in Packet
Day 6: Solving Rational Expressions using the LCD ……………………………………….…………Page 34
HW: Page 38 in Packet
Day 7: Review of Adding /Subtracting and Solving Rational Expressions using the LCD .…………Page 39
HW: Pages 39 – 42 in Packet
Day 8: QUIZ
Day 9 – Review
Pages 43 – 49 in Packet
Day 10 - Test
2
Chapter 12 – 3 (Day 1)
SWBAT: Simplify rational expressions and identify excluded values of rational expressions.
Warm – Up
Reduce to lowest terms.
14x2
a.
2x
b.
3x5
a.
c.
6x3
30x
15x3y25
6x2y43
35x
Example 1: Find the value for x that makes the fraction undefined (excluded values):
6
a.
x+4
3
b.
3x-6
c.
2x+1
x2- 15x
Practice: Find the value for x that makes the fraction undefined (excluded values):
3
Example 2: Reduce to lowest terms (factoring and cancelling).
a)
2x-10
2x
=
4x-8
3x-15
b)a)
4x
x-5
=
Think:
5x-15
4x-6
c)
3)
5x
2x-3
=
Practice: Reduce to lowest terms.
1)
=
10x-20
10
2)
3x-9
3x
6x-12
4x-12x
b)
** 3) x-2
4x
=
4
Think:
Example # 3: Reduce to lowest terms (factoring trinomials and cancelling).
a)
x+5
b)
x2+4x-5
x-1
x2-2x+1
=
=
Practice: Reduce to lowest terms.
1)
x+3
2)
x2-x-12
x+1
x2+5x+4
=
=
Example 4: Reduce to lowest terms (factoring numerator and denominator)
2x-4
x2-4
a)c) x22+4x-12
x -8x+12
b)
Think:
x2-25
x2+10x+25
Practice: Reduce to lowest terms
1)
x2-4
x2+4x+4
**
2)
3)
x2-25
5x+5
xx22+2x-15
-4x-5
5
Example 6: Recognize Opposites. Simplify if possible and state the excluded values
Case 1:
Case 2:
Case 3:
Note:
__________________________________________________________________________________________
__________________________________________________________________________________________
Example:
Practice:
=
=
6
Challenge Problem:
Simplify.
2)
4x-x2
x2-16
Summary:
Exit Ticket:
7
Homework (Day1)
Reduce to lowest terms (factoring and cancelling).
8
Reduce to lowest terms (factoring and cancelling).
16)
17)
18)
19)
9
Chapter 12 – 4 (Day 2)
SWBAT: Multiply and Divide rational expressions
Warm – Up
1. Gfg
2.
=
=
=

=
=
10
Practice: Find the product in lowest terms.
24x 3 14y
1) 24x  y2 21z2
6) 35y 3 8x
12xy
7z

11
Practice: Find the product in lowest terms.

Part 3: Multiply Rational Expressions Involving Trinomial Polynomials.
=

12
Practice

=
Part 4: Multiply a Rational Expression by a Polynomial.

=
Practice
=

13
Part 5: Divide Rational Expressions involving Polynomials.
=

Practice
=
=

14
Part 6: Divide Rational Expressions by a Polynomial.
=
=

Practice
a) fdfdf

15
Challenge Problem: Find the product in lowest terms.
Summary:
Exit Ticket:
16
Day 2: Homework
Multiply and reduce to simplest form.
1.
2.
3.
4.
5.
6.
7.
8.
17
Divide and reduce to simplest form.
9.
10.
11.
12.
14.
13.
15.
16.
18
Day 3 – Review of Simplifying, Multiplying and Dividing Rationals
19
20
21
22
ADDING AND SUBTRACTING RATIONALS (Day 4)
SWBAT: To add and subtract rational expressions with the same denominators.
Warm _Up
1. Add and simplify your answer.
QUIZ
4 2
a)
+
9 9
b)
4x 2x
+
9
9
5 1
c)
+
6 6
Example 1: Add the fractions and reduce to lowest terms.
2. Subtract and simplify your answer.
7
1
a)
12 12
a) 3b
b2
+
5b
b2
7x x
b)
12 12
c)
7
1
12x 12x
c) 2m + 4
m2 - 9
+
2
m2 - 9
23
Practice: Add the fractions and reduce to lowest terms.
1)
2x 4x


8
8
2)
19c 9c


12 d 12 d
3)
x
3
 2

x 9 x 9
4)
2x
6


x3 x3
2
Example 2: Subtract the fractions and reduce to lowest terms.
a) 10x 2x
5y 5y
b) 5a + 2
a2 - 4
-
2a - 4
a2 - 4
c)
3m - 6
m2 + m - 6
-
-m + 2
m2 + m - 6
24
Practice: Subtract the fractions and reduce to lowest terms.
7) 11b
3y

4b

3y
9) 6 x  5
x2 1

5x  6

x2 1
8) 8 x  4
2x  6

4x  6

2x  6
10)
Challenge Practice:
13)
x 2  2 xy xy  2 y 2


x  2y
x  2y
25
Summary:
Exit Ticket:
26
Homework - (Day 4)
Add or Subtract. Simply your answer.
1)
3)
x
5x
 2 
2
3x
3x
x
4
 2

x  16 x  16
2
5)
7
3
 3 
3
2x
2x
7) 3 x  x
2x2  2x


2x  2
2x  2
2
9)
4 x  13
1
 2

x  5x  6 x  5x  6
2
2) 4 y
y3

4y

y3
4) x 2  12
x3
6)
8)
10)

3

x3
x2
6x


x6 x6
x3
c 8
 2

2
4 x  25 4 x  25
7x  2
5x  6
 2

x  3x  2 x  3x  2
2
27
Adding and Subtracting Rationals (Day 5)
SWBAT: To add and subtract fractions with unlike denominators.
Warm Up
Add and simplify your answer.
3x  8 2 x  7
 2

2
x 9 x 9
28
Part 1: Identifying LCM
Find the LCM of the given expressions
A.
Practice:
***3.
29
(
)
(
)
(
)
(
)
30
Practice: Add or Subtract.
31
Challenge Problem: Add or subtract and simplify your answers.
Summary:
Exit Ticket:
32
Homework- (Day 5)
Add or subtract. Simplify your answer.
33
Chapter 12 – 7 Solving Rational Equations (Day 6)
SWBAT: Solve Rational Expressions by Using the LCD.
Warm Up
1. Gfdg
2.
Solving a Rational Equation
Example 1: Solve.
Practice
1)
2)
34
Example 2: Solving a Rational Equation
x 3x 7


10 5 2
Step 1: Find the LCD
Step 2: Multiply every term by the LCD
Step 3: Simplify and solve.
Practice: Solve. Check your answer.
3)
x 1 1
 
6 3 2
4)
5x 1
 2
8 2
35
Example 3: Solve. Check your answer.
5 1 1
 
3x 9 x
Practice: Solve. Check your answer.
5)
6)
36
Challenge Problem: Solve. Check your answer.
9
9
+
= 12
x x-2
Summary:
Exit Ticket:
37
Homework (Day 6)
Solve. Check your answer.
1)
3)
2)
1 2 5


x 3x 6
4)
5)
6)
7)
8)
8 x x  1 x  15


3
4
6
38
Day 7 – Review of Adding/Subtracting and Solving Rational Equations
39
40
25-30) Simplify each rational expression by adding/subtracting. Box your answers and
factor/simplify at the end, if need be.
25.
26.
27.
28.
29.
30.
31-39)
41
40-47)
40.
41.
40.
41.
42.
43.
42.
43.
44.
45.
44.
45.
46.
47.
46.
47.
42
Day 8 – TEST REVIEW
Section 1: Excluded Values
Section 2: Simplifying Rational Expressions
43
Section 3: Multiplying and Dividing Rational Expressions
44
Section 4: Adding and Subtraction with Like Denominators
Section 5: Adding and Subtraction with Unlike Denominators
45
Section 6: Solving Rational Equations
F.O.I.L. on the left and Distribute on the right
Set Quadratic Equation equal to zero.
Factor out GCF
Set up a “T” chart and solve for x.
Solve each equation. Check your answer
Step 1: Find the LCD
Step 2: Multiply everything by the LCD
Step 3: Simplify and Solve.
46
More Practice!
47
48
49