Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 33: Adding and Subtracting Rational Expressions
Answer/Discussion
to 1a

The first denominator has the following factor: 
The second denominator, 5  x, looks
like the first denominator except the signs are switched. We can
rewrite this as 
Putting all the different factors together and using the highest
exponent, we get the following LCD: 
Note that I did not put the 1 that was in front of the second denominator's
(x  5) factor. In the step 3, I will put the negative into the problem
by placing it in the numerator of that second fraction. 
Now the two fractions have a common denominator, so we do not have
to rewrite the rational expressions. 

*Combine the two num.
*Write over the common den.


*Divide out the common factor of (x 
5) 
Answer/Discussion
to 1b

The first denominator has the following factors: 
The second denominator has the following factor: 
Putting all the different factors together and using the highest
exponent, we get the following LCD: 
Since the first rational expression already has the LCD, then
we do not need to change this fraction. 

*Rewriting denominator in factored form

Rewriting the second expression with the LCD: 

*Missing the factor of (a 
2) in the den.
*Mult. top and bottom by (a  2)


*Combine the two num.
*Write over the common den.


*Divide out the common factor of (a  3) 
Answer/Discussion
to 1c

The first denominator has the following factor: 
The second denominator has the following factors: 
The third denominator has the following factors: 
Putting all the different factors together and using the highest
exponent, we get the following LCD: 
Rewriting the first expression with the LCD: 

*Missing the factors 2 and x in the den.
*Mult. top and bottom by 2x

Rewriting the second expression with the LCD: 

*Missing the factor of x in the den.
*Mult. top and bottom by x

Rewriting the third expression with the LCD: 

*Missing the factor of 2 in the den.
*Mult. top and bottom by 2


*Combine the three num.
*Write over the common den.


*Divide out the common factor of (x + 2)

Last revised on July 17, 2011 by Kim Seward.
All contents copyright (C) 2001  2011, WTAMU and Kim Seward.
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