Lesson Page

 

Simplifying Algebraic Fractions
 Math B

 

To simplify an algebraic fraction means to reduce it to lowest terms.  We do this by dividing out the common factors in the numerator
and the denominator.

Example 1
Simplify:

First factor the numerator and factor
the denominator.


 

Then divide out the common binomial
factor (x+2).


 
Final Answer:

 

 

Example 2
Simplify:
Again, factor the numerator and
         factor the denominator.


 
Divide out the common binomial
          factor of  (y-2)


 
Divide out the common monomial
            factor of  2y

 

Final Answer: 

   

Example 3
 
Simplify:

 

 

Factor the numerator and factor the denominator.


 
Notice how factoring (-1) will allow for the division of the common binomial factor of (x-2).


 
Final Answer:   or

 

 

Enrichment topic:  Not tested on Math B.

Factoring Cubes: 

 

Example 4


 

Need more help factoring this problem?
Factoring Help for Example 4
 
Factor the numerator and
           denominator.

Divide out the common binomial
           factor of  (y+5)

Final Answer: 

 

 

Factoring is a critical skill for simplifying fractions. For additional help see the Math A site on Factoring.

 

 


Murray