Multiplication of Rational (Fractional) Expressions
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Simply Put:
The rule for multiplying algebraic fractions
 is the same as the rule for multiplying numerical fractions.

Multiply the tops (numerators)
 AND
multiply the bottoms (denominators).

 

The Rule:


 

If possible, reduce (cancel) BEFORE you multiply the tops and bottoms!
(It's easier than simplifying at the end!)


EXAMPLES


Multiply and express the product in simplest form:

1.
                      

 

CAUTION:

You can only cancel top with bottom or bottom with top.

There is NO canceling bottom with bottom or top with top!

 

2. 
                               

Remember to factor first if possible.

3.  



 

Factor everything that can be factored.






 

Cancel (bottom with top or top with bottom).


 

Multiply tops (numerators) and bottoms (denominators).