Lesson 2
1. Lesson 2
1.8. Explore 4
Module 6: Rational Expressions
Turn to page 325 in your textbook. Read “Dividing Rational Expressions,” above “Example 2.” Examples are shown using both rational numbers and rational expressions. As you read this section, think about the relative benefits and drawbacks of each method shown. Answer the following questions:
- Is one method better for identifying non-permissible values?
- Which method do you prefer? Explain why.
- Notice that the x-variable appears in neither the denominator in the original expression nor in the denominator in the final simplified form. Yet x ≠ 0. In other words, x = 0 is a non-permissible value. What does this tell you about how you should identify non-permissible values?
Dividing rational expressions is similar to dividing rational numbers. One difference is that, in the case of rational expressions, you must state the non-permissible values.
When dividing rational expressions, however, the non-permissible values must be determined by considering where the denominators of the original expression are equal to zero. To be sure that you have included all non-permissible values, you must consider the denominators of the simplified form and the denominators throughout the division process. Keep this in mind as you proceed to the next activity.
Try This 5
- Solve the following rational expression.
- Identify the non-permissible values.
Refer to “Example 2” on page 325 of your textbook to confirm that you correctly simplified and identified all of the non-permissible values.
Save your response in your course folder.
Did You Know?
A complex rational expression is a rational expression that contains rational expressions in the numerator and/or denominator. Here is an example:
A complex rational expression doesn’t have to be intimidating! You can write the preceding example in the following way:
You can then factor and simplify as usual.
Share 3
With a classmate, discuss the following points related to Try This 5.
- Why is it important to factor any second-degree polynomial?
- Where do you look for non-permissible values?
- Why are division expressions first converted to multiplication expressions before simplifying?
Save your response in your course folder.
Self-Check 2
Complete Dividing Rational Numbers Self-Check.
