**Learning Objectives**

After completing this tutorial, you should be able to:

- Simplify complex fractions.

** Introduction**

**Are
fractions getting you down?** If so, you are not alone.
Well, you are in luck. We have one more tutorial devoted to rational
expressions
(fractions). In this tutorial we will be looking at simplifying
complex
fractions. If you need a review on simplifying and dividing
rational
expressions, feel free to go back to **Tutorial
32: Multiplying and Dividing Rational Expressions**. If you need a
review on finding the LCD of fractions feel free to go back to **Tutorial
33: Adding and Subtracting Rational Expressions**. It is time to
get started with this tutorial.

** Tutorial**

In other words, there is at least one small fraction within the overall fraction.

**Some examples of complex fractions are:**

and

There are two ways that you can simplify complex fractions. We will call them method I and method II.

In other words, you will be combining all the
parts of the numerator
to form one fraction and all of the parts of the denominator to form
another
fraction. If you need a review on adding and subtracting rational
expressions, go to **Tutorial 33:
Adding
and Subtracting Rational Expressions.**

**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.**

If you need a review on simplifying rational
expressions, go to **Tutorial
32: Multiplying and Dividing Rational Expressions.**

**AND**

**Step 3: If needed, simplify
the rational expression.**

***Divide out a common factor of 4**

**AND**

**Step 3: If needed, simplify
the rational expression.**

***Divide out common factors of a and b**

Recall that when you multiply the exact same
thing to the numerator
and the denominator, the result is an equivalent fraction. If you
need a review on finding the LCD, go back to **Tutorial
33: Adding and Subtracting Rational Expressions.**

**Step 2: If needed, simplify
the rational expression.**

Putting all the different factors together and using
the highest exponent,
we get **the following LCD** for all the small fractions:

***Divide out the common factor
of (2 x + 1)**

Putting all the different factors together and using
the highest exponent,
we get **the following LCD** for all the small fractions:

***Divide out the common factor
of (3 y + 1)**

At first glance, this does not look like a complex
fraction. **However,
once you rewrite it with positive exponents you will see that we really
do have a complex fraction.**

***Rewrite with positive exponents**

and

Putting all the different factors together and using
the highest exponent,
we get **the following LCD** for all the small fractions:

***Factor
out the GCF of ab in the num.**

** Practice Problems**

These are practice problems to help bring you to the
next level.
It will allow you to check and see if you have an understanding of
these
types of problems. **Math works just like
anything
else, if you want to get good at it, then you need to practice
it.
Even the best athletes and musicians had help along the way and lots of
practice, practice, practice, to get good at their sport or instrument.**
In fact there is no such thing as too much practice.

To get the most out of these, **you should work the
problem out on
your own and then check your answer by clicking on the link for the
answer/discussion
for that problem**. At the link you will find the answer
as well as any steps that went into finding that answer.

Practice Problems 1a - 1b:Simplify.

** Need Extra Help on these Topics?**

**Go to Get
Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for
some
more suggestions.**

Last revised on July 17, 2011 by Kim Seward.

All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.