Last time, we learned how to simplify a mixed expression. Let’s review with some examples.

Find the simplified rational expression for the given mixed expression.

Click the “Submit” button after selecting your answer.

Now, let’s move on with today’s lesson.

Look at this fraction. The numerator and denominator both contain fractions.

The numerator <EQUATION> is a rational expression.

The denominator <EQUATION> is also a rational expression.

This expression is called a complex fraction.

We simplify a complex fraction by multiplying the expression in the numerator by the reciprocal of the divisor.

In this case the divisor is the expression in the denominator.

What is the simplified form of this complex fraction? Click the “Submit” button after selecting your answer.

We multiply the two rational expressions.

Then, we simplify the result by canceling out common factors x and y.

The simplified result is 2xy.

Here we have a fraction with the mixed expression <EQUATION> in the numerator.

The denominator is the rational expression <EQUATION>

In order to simplify this fraction, we first need to rewrite the numerator as a single rational expression.

What is the simplified form of the numerator? Click the “Submit” button after selecting your answer.

We rewrite the numerator as the rational expression: <EQUATION>

We now can simplify this complex fraction by multiplying <EQUATION> by the reciprocal <EQUATION>.

What is the simplified form of the complex fraction? Click the “Submit” button after entering your answer.

The simplified form of the complex fraction is just c.

Now, look at this fraction.

We have the rational expression <EQUATION> in the numerator.

The mixed expression <EQUATION> is in the denominator.

What is the simplified form of this fraction? Click the “Submit” button after selecting your answer.

First, we rewrite the denominator as the single rational expression: <EQUATION>.

We then simplify the complex fraction by multiplying by the reciprocal: <EQUATION>.

The result is <EQUATION>.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education