Lesson 4
1. Lesson 4
1.9. Explore 5
Module 6: Rational Expressions
Working with Quadratic Denominators
Some rational equations contain denominators that are quadratic expressions. In these cases, a good approach for finding the LCD is to factor the denominators first.
Another good practice in solving rational equations is to check your solution. Do the roots satisfy the original equation? If not, is it because a root is extraneous or is it because an error was made when solving the equation?
Read through “Example 1” on pages 342 to 343 in the textbook. As you read, pay attention to the following points:
- How is the LCD determined?
- How is the equation simplified?
Self-Check 2
- Complete “Your Turn” on page 343 of the textbook. Answer
- Complete “Your Turn” on page 344 of the textbook. Answer
In Share 2 you discovered it is possible to obtain a root of a rational equation that also happens to be a non-permissible value. When this occurs, the root is considered extraneous. If you obtain an extraneous root, it does not necessarily mean that you have done something wrong. In fact, extraneous roots can be obtained even if you do not make any errors.
Turn to “Example 2” on page 344 of the textbook. On this page you will find a rational equation that appears to have two roots. In fact, one of the roots is extraneous. Work through the example and try to find out how it is possible for an extraneous value of the variable to be obtained.
Self-Check 3
Complete “Practice” question 3 and “Apply” question 6 on page 348 of the textbook. Answer