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Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 34: Complex Fractions


checkAnswer/Discussion to 1a

problem 1a


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


Step 3: If needed, simplify the rational expression.


*Rewrite div. as mult. of reciprocal

*Divide out a common factor of 2




checkAnswer/Discussion to 1b

problem 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:

ad1b2  and ad1b3

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





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



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Last revised on July 17, 2011 by Kim Seward.
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