Lesson 4

Lesson 4 Summary

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In this lesson you investigated the following questions:

• What principles are common to the strategies for solving rational equations and how are these principles helpful?
  
  
• 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. Watch Steps for Solving Rational Equations for a visual of this process.

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.