Simplifying Rational (Fractional) Expressions
Topic Index | Algebra2/Trig Index | Regents Exam Prep Center


To simplify an algebraic fraction means to reduce it to lowest terms.
This is done 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