Learning Objectives
Introduction
Do you ever feel like running and hiding when you see a fraction? If so, you are not alone. But don't fear! Help is here! Hey, that rhymes. Anyway, over the next several tutorials we will be showing you several aspects of rational expressions (fractions). In this section we will be simplifying them. Again, we will be putting your knowledge of factoring to the test. Factoring plays a big part of simplifying these rational expressions. We will also look at multiplying and dividing them. I think you are ready to tackle these rational expressions.
Tutorial
A rational
expression or function
is
one that can be written in the form
where P and Q are polynomials and Q does not equal 0.
With rational functions, we need to watch out for values that cause our denominator to be 0. If our denominator is 0, then we have an undefined value.
So, when looking for the domain of a given rational function, we use a back door approach. We find the values that we cannot use, which would be values that make the denominator 0.
So to find our domain, we want to set the denominator “not equal” to 0 to restrict those values.
*"Solve" for x
*"Solve" for x
For any
rational expression ,
and
any polynomial R, where ,,
then
This will come in handy when we simplify rational expressions, which is coming up next.
Simplifying (or reducing) aTutorial 27: The GCF and Factoring by Grouping
Tutorial 28: Factoring Trinomials
Tutorial 29: Factoring Special Products
AND
Step 2: Divide out all common factors that the numerator and the denominator have.
*Divide out the common factor of (x + 10)
Multiplying Rational Expressions
Q and S do not equal 0.
Tutorial 27: The GCF and Factoring by Grouping
Tutorial 28: Factoring Trinomials
Tutorial 29: Factoring Special Products
AND
where Q, S, and R do not equal 0.
Step 2: Multiply the rational expressions as shown above.
AND
Step 2: Multiply the rational expressions as shown above.
*Factor the num. and den.
*Div. out the common factors
of
(t +
3) and (t - 2)
*Factor the num. and den.
*All factors divide out
Practice Problems
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 Problem 1a: Find the domain of the rational function.
Practice Problems 2a - 2c: Multiply or divide.
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.