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Multiplying or Dividing Rational Expressions

Multiplying or Dividing Rational Expressions

The basic rule for multiplying fractions is to multiply the numerators together and then multiply the
numerators together

and the reduce the answer .

It is often much faster if we first reduce the fractions first . This is done by factoring each part and then
canceling common factors .

Example 1   Example 2  
   
factor each numerator
factor each denominator
factor each numerator
factor each denominator
cancel all common factors cancel all common factors
   

Multiplying Rational Expressions

We multiplying Rational Expressions the same way we multiply any fraction To do this we fist
completely factor all the numerators and denominators and then cancel out all the common factors.

1, Completely factor all the the numerators and denominators.

2. Cancel out the common factors.

3. Write the remaining factors in fraction form

Example 3

 
factor each numerator
factor each denominator
cancel all common factors  
 
Example 4  
 
factor each numerator
factor each denominator
cancel all common factors  
 
Example 5  
 
factor each numerator
factor each denominator
cancel all common factors  
 
Example 6  
 
factor each numerator
factor each denominator
cancel all common factors  
 

Dividing Rational Expressions

We divide Rational Expressions like

by changing the division problem into a multiplication problem. We do this by inverting (flipping
over) the second fraction and change the problem to multiplication.

1. Invert the second fraction and change the problem to multiplication.
2. Completely factor all the the numerators and denominators.
3. Cancel out the common factors.
4. Write the remaining factors in fraction form

Example 7

Invert the second fraction and multiply
 
factor each numerator
factor each denominator
cancel all common factors  
 

Example 8

Invert the second fraction and multiply
 
factor each numerator
factor each denominator
cancel all common factors  
 

Example 9

Invert the second fraction and multiply
 
factor each numerator
factor each denominator
cancel all common factors  
 
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