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


Answer/Discussion to 1a


 
Step 1: Find the LCD as shown in tutorial 10.

 
The first denominator has the following two factors:

 
*Factor the trinomial

 
The second denominator has the following two factors:

 
*Factor the trinomial

 
Putting all the different factors together and using the highest exponent, we get the following LCD:

 

 
Step 2: Write equivalent fractions using the LCD if needed.

 
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)

 

 
 
Step 3: Combine the rational expressions as shown in tutorial 10.

 

 

*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.

 
(return to problem 1a)


 

Answer/Discussion to 1b


 
Step 1: Find the LCD as shown in tutorial 10 if needed.

 
The first denominator has the following two factors:

 
*Factor the difference of squares

 
The second denominator has the following factor:

 

 
Putting all the different factors together and using the highest exponent, we get the following LCD:

 

 
Step 2: Write equivalent fractions using the LCD if needed.

 
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)

 

 
 
Step 3: Combine the rational expressions as shown in tutorial 10.

 
*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.

 
(return to problem 1b)

 

 

WTAMU > Virtual Math Lab > College Algebra > Tutorial 10: Adding and Subtracting Rational Expressions


All contents copyright (C) 2002 - 2008, WTAMU and Kim Seward. All rights reserved.
Last revised on April 2, 2008 by Kim Seward.