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Answer/Discussion to 1a

 

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

 

Combining only the numerator we get:

 

*Rewrite fractions with LCD of 10

 

Combining only the denominator we get:

 

*Rewrite fractions with LCD of 6

 

Putting these back into the complex fraction we get:

 

*Write numerator over denominator

 

Step 2:  Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator AND Step 3: If needed, simplify the rational expression.

 

*Rewrite div. as mult. of reciprocal     *Divide out a common factor of 2

 

(return to problem 1a)

 

 

Answer/Discussion to 1b

 

Rewriting the expression with positive exponents, we get:

 

*Rewrite with positive exponents

 

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

 

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

 

x and y

 

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

 

and

 

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

 
 

Multiplying numerator and denominator by the LCD we get:

 

*Mult. num. and den. by x squared y squared

 

Step 2: If needed, simplify the rational expression.

 

*Factor out the GCF of 2xy in the num. *Den. factors as a difference of two squares

 

(return to problem 1b)

 

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