The document provides instruction on simplifying rational expressions and equations, including complex fractions. It reviews concepts like multiplication and division of rational expressions, addition and subtraction of rational expressions, finding the lowest common denominator, and working with complex fractions. Examples are provided to demonstrate these concepts and techniques for simplifying rational expressions and solving rational equations.

1. Today:
 Review: Rational Expressions
& Equations
 Complex Fractions
 Test: Simplifying Rational
Expressions

2. 3
2
9
10 21
x x
x x

 
2
( 9)
( 7)( 3)
x x
x x

 
( 3)( 3)
( 7)( 3)
x x x
x x
 
 
( 3)( 3)
( 7)( 3)
x x x
x x
 
 
Simplifying:
( 3)
( 7)
x x
x



3. Excluded
Values:

4. Multiplication &
Division:

5. bd
ac
d
c
b
a

62
5
15
3



x
x
)62)(15(
)5)(3(



x
x
)3)(2)(15(
)5)(3(



x
x
3
)2)(3(
1

6
1

Multiplication &
Division:

6. Addition &
Subtraction:
2
4
1
2


 xx
)2)(1( 

xx
The denominators don’t
share any factors
)2(2 x )1(4  x
)2)(1(
6


xx
x
Find the LCD

7. Subtraction:
bd
bcad
d
c
b
a 

4
33
2
12 

 xx
)4)(2(
)33(2)12(4 

xx
8
6648 

xx
8
22 

x
8
)1(2 

x
4
4
1

x

8. Equations:

9. Complex
Fractions:

11. Need:
Pencil
Scratch Paper
Correct Code
No Phones,
Calculators
not necessary