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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)

 

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Last revised on Dec. 15, 2009 by Kim Seward.
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