Multiplying and Dividing Algebraic Fractions
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Multiplication and division of algebraic fractions is actually an extension of reducing fractions, except that now there are two fractions in the problem instead of just one. 

Factor first if possible.  Then reduce common factors between any numerator and denominator.  

Reducing may be done up-down, NOT across (horizontally).  
 

 Multiply:   

Solution:  Look for possible items to reduce - one from the top with one from the bottom.  Expanding the exponents may be helpful if you are having trouble working with powers.

Remember to reduce "up-down" (one in the top with one in the bottom).  Reduce the variables, remembering to leave the remaining variables where the larger exponent occurred.


The answer is: 
 


 
 Multiply:   

Solution:  Look for possible items to reduce.  In this problem,
the numerator in the first term can be factored more than once.

Now reduce:

Final answer:


 

 

  Divide:

Remember that with division, it is necessary to "flip" the second fraction and change the operation to multiplication (just as you did with "regular number" fractions in elementary school).

First, FLIP the second fraction and change the operation to multiply:

Answer: 

 

  Divide:

Again, remember that with division, it is necessary to "flip" the second fraction and change the operation to multiplication.

First, FLIP the second fraction and change the operation to multiply:

Factor first:


Reduce:

Answer: