Answer/Discussion on Complex Fractions

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Intermediate Algebra
Answer/Discussion to Practice Problems
on Complex Fractions

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

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.

(Back to the tutorial on complex fractions)