Lesson 4

Lesson 4 Summary

 

In this lesson you investigated the following questions:

• What are the different strategies used, and how are they helpful in solving rational equations?
• Why are some values of the variable that are obtained in solving rational equations not roots of the equations?

You discovered that solving rational equations is like solving puzzles. The approach taken should simplify the overall task. In the case of rational equations, clearing the denominators is a good way to simplify the task. By doing so, you are left with either a linear or a quadratic equation to solve. Solving for the unknown in a rational equation is not the last step. Extraneous roots occur when the value of the variable obtained is also a non-permissible value. Non-permissible values are unique to rational expressions where a variable occurs in the denominator. However, since the solution process involves solving an equivalent non-rational equation (with no denominators; hence, no restrictions), it is possible for an extraneous solution to be obtained.

 

In the next lesson you will learn how to model problems with rational equations. You will use the strategies you developed in this lesson to solve those problems.