Simplifying rational expressions involves factoring the numerator and denominator and cancelling out any common factors between them. A rational expression is in simplest form when the numerator and denominator have no common factors other than 1. To simplify a rational expression, you factor the numerator and denominator completely and cancel out any common factors.

1. •SIMPLIFYING
RATIONAL
EXPRESSION

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

3. 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

4. Simplifying Rational Expressions
• 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:

5. Simplifying Rational Expressions
• 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



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

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

8. 1
2
3
:
Simplify 2
2



y
y
y
  
  
1
1
2
1




y
y
y
y
1
2



y
y

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

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

11. 2
2
9
Simplify:
2 15
a
a a

 
  
  
3 3
5 3
a a
a a
 
 
1
2
1



a
a

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