Complex Fractions

What we call a complex fraction in this section is a fraction made up of one or more fractions.
Since the word complex is generally reserved for a concept you'll learn in College Algebra , a
more accurate description of what you'll see in this section is complicated fractions. This type of
fraction is one in which you have at least one fraction in the numerator or denominator (or both).

Examples:

The instructions for working with these types of fractions are " simplify the following " or just
" simplify ." The method we will employ for working these out is to work out the numerator and
denominator separately until we get just one fraction (or monomial) in each. Then we do the
division by multiplying the numerator by the reciprocal of the denominator.

Steps to simplifying complex fractions:
1. Get one fraction or monomial in each of the numerator and denominator.
2. Multiply the numerator by the reciprocal of the denominator.
3. Simplify
a. Factor (if necessary) and cancel
b. Leave your answer in factored form

Examples:
Simplify the following :

(1) done

(1) done

Steps:

(1) done

Steps:

(1) done

Steps:

(1) done

Steps:

Steps: Rewrite: