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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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