3 6 Title

Intermediate Algebra
Tutorial 34: Complex Fractions

 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

 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

Last revised on July 17, 2011 by Kim Seward.