The Extraneous solutions to rational equations exercise appears under the Algebra II Math Mission. This exercise solves equations and experiments with understanding extraneous solutions.
Types of Problems[]
There are two types of problems in this exercise:
- Find the solution(s) to the rational equation: This problem has a rational equation that possibly has some extraneous solutions. The student is expected to solve the equation and determine if any of the solutions were actually extraneous.
- Determine if there is an extraneous solution: This problem has a rational equation and a possible extraneous solution. The student is asked to determine if the given value is a solution, an extraneous solution or nothing.
Strategies[]
Knowledge of basic rational equations and a motivation to "check" answers are encouraged to ensure success on this exercise.
- The equations conveniently have the same denominator. Ignore the denominator, solve the resulting quadratic for the initial solutions.
- Extraneous solutions are initial solutions to an equation that are restricted due to some domain restriction.
- Not being a solution is not the same as being an extraneous solution.
- Extraneous solutions occur because operations are performed on an equation that do not (necessarily) maintain equality.
Real-life Applications[]
- Rational equations are used to solve certain work rate and distance word problems.
- Extraneous solutions occur frequently with restricted domains. They are subtle but important in some applications.
- Extraneous solutions not only happen with rational equations, but also with radical equations.