Michigan Algebra I Sept. 2012

Sometimes when solving math problems the process of simplifying creates a different domain than the original equation. This creates an invalid solution known as extraneous. An extraneous solution is the solution of the simplified form of an equation that does not satisfy the original equation and needs to be eliminated.

It is necessary to check for extraneous solutions when the original equation has a restricted domain. The equation in the next example contains a square root. Since even root functions are restricted to values greater than or equal to zero, any equation involving even roots or their corresponding fractional exponent should be checked for extraneous solutions.

There are other functions that require checks of extraneous solutions, but those will be discussed in other courses.