College Algebra Tutorial 11


College Algebra
Answer/Discussion to Practice Problems  
Tutorial 11: Complex Rational Expres
sions


WTAMU > Virtual Math Lab > College Algebra > Tutorial 11: Complex Rational Expressions


 

 

check markAnswer/Discussion to 1a

problem 1a
 

Step 1:   If needed, rewrite the numerator and denominator so that they are each a single fraction.

 
Combining only the numerator we get:

 
ad1a1
*Rewrite fractions with LCD of y
 
 

 
 

Combining only the denominator we get:

 
ad1a2
*Rewrite fractions with LCD of y
 

 
 

Putting these back into the complex fraction we get:

 
ad1a3

*Write numerator over denominator

 
Step 2:  Divide the numerator by the denominator

AND

Step 3: If needed, simplify the rational expression.
 

ad1a4

*Rewrite div. as mult. of reciprocal
 
 

*Divide out a common factor of y
 
 
 
 

*Excluded values of the original den.
 

Note that the values that would be excluded from the domain are 0 and -1/2.  These are the values that make the original denominators equal to 0.

 
(return to problem 1a)


 

 

check markAnswer/Discussion to 1b

problem 1b
 

Step 1: Multiply the numerator and denominator of the overall complex fractions by the LCD of the smaller fractions.

 
The denominators of the numerator's fractions have the following factors:

 
ad1b1
ad1b2

 
The denominators of the denominator's fractions  have the following factors:

 
ad1b3

ad1b4
 

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

 
ad1b5

 
Multiplying numerator and denominator by the LCD we get:

 
ad1b6

*Mult. num. and den. by x(x +3)
 
 
 
 
 
 
 
 
 
 

 
 
 

Step 2: If needed, simplify the rational expression.

 
ad1b7

 

*Factor the GCF of 2
*No common factors to divide out
 

*Excluded values of the original den.
 

Note that the values that would be excluded from the domain are 0, -3 and -7/2.  These are the values that make the original denominators equal to 0.

 
(return to problem 1b)

 

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WTAMU > Virtual Math Lab > College Algebra > Tutorial 11: Complex Rational Expressions


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