Simplifying Rational (Fractional) Expressions
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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