College Algebra
Answer/Discussion to Practice Problems
Tutorial 10: Adding and Subtracting Rational Expressions
Answer/Discussion
to 1a

The first denominator has the following two factors: 
The second denominator has the following two 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 factor of (a
+ 7) in the den.
*Mult. top and bottom by (a
+ 7)

Rewriting the second expression with the LCD: 

*Missing the factor of (a +
9) in the den.
*Mult. top and bottom by (a +
9)


*Combine the numerators
*Write over common denominator

Step 4: Reduce to lowest terms. 
This rational expression cannot be simplified down any farther. 
Also note that the values that would be excluded from the domain
are 9, 3 and 7. These are the values that make the original
denominator equal to 0. 
Answer/Discussion
to 1b

The first denominator has the following two 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, we
do not need to change this fraction. 

*Rewriting denominator in factored form

Rewriting the second expression with the LCD: 

*Missing the factor of (x 
7) in the den.
*Mult. top and bottom by (x 
7)


*Combine the numerators
*Write over common denominator
*Distribute the minus sign through the (
)

Step 4: Reduce to lowest terms. 
This rational expression cannot be simplified down any farther. 
Also note that the values that would be excluded from the domain
are 7 and 7. These are the values that make the original
denominator equal to 0. 
Last revised on Dec. 15, 2009 by Kim Seward.
All contents copyright (C) 2002  2010, WTAMU and Kim Seward. All rights reserved.

