10_1 Simplifying Rational Expressions Trout 09.ppt

10.1 Simplifying Rational
Expressions
• Goal: factor and cancel out common factors
in the numerator and denominator

Simplifying Rational Expressions
• A “rational expression” is the quotient of
two polynomials. (division)
2
2

n
n
2
3
10
3
2



x
x
x

• A rational expression is in simplest form
when the numerator and denominator have
no common factors (other than 1)
15
9
Simplify
5
3
3
3



5
3

REVIEW:

• Factors and addends
are different
• Factors are things
multiplied together
• Addends are things
added together
CAN ONLY CANCEL
OUT FACTORS
5
3
3
3
Simplify



How to get a rational expression in
simplest form…
• Factor the numerator completely
• Factor the denominator completely
• Cancel out any common factors (not
addends)

x
x
5
10
5
:
Simplify
  
x
x
5
2
5 

Factor
 
x
x 2


x
x 2



1
2
3
:
Simplify 2
2



y
y
y
  
  
1
1
2
1




y
y
y
y
1
2



y
y

y
y
48
24
12
:
Simplify

  
  
y
y
4
12
2
12 
y
y
4
2



x
x
x
x
2
3
2
:
Simplify 2
2


  
  
2 1
3 2
x x
x x


2 1
3 2
x
x




2
2
9
Simplify:
2 15
a
a a

 
  
  
3 3
5 3
a a
a a
 
 
1
2
1



a
a

x
x


4
4
:
Simplify
 
  
4
1
4



x
x
1
1
1





Mrs. Rodriguez’s Shortcut
a-b = -1
b-a

10_1 Simplifying Rational Expressions Trout 09.ppt

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10_1 Simplifying Rational Expressions Trout 09.ppt