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Simplifying Rational Expressions    [Show All Solutions]

Simplify each of the following rational expressions.

 

1.  

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There isn’t a lot to these problems.  Just factor the numerator and denominator as much as possible then cancel all like terms.  Recall that you can only cancel terms that multiply the whole numerator and whole denominator.  In other words, you can’t just cancel the  and you can’t cancel a 4 from the 8 in the numerator and the 4 in the denominator.  Things just don’t work this way.

 

If you need convincing of this consider the following number example.

 

 

Here is the answer to this problem.

 

 

2.  

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In this one you’ve got to be a little careful.  First factor the numerator and denominator.

 

 

At first glance it doesn’t look like anything will cancel.  However remember that

 

 

Using this on the term in the denominator gives the following.

 

Also recall that

 

 

so it doesn’t matter where you put the minus sign.

 

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