What Is an Extraneous Solution?

Extraneous solutions are roots that come from transformations of equations but are not applicable to the original equation. The reason for the exclusion is that the original domain does not include the root from the transformed equation.

In the equation (2/x-4) + (2/x+4) = [8/(x-4)(x+4), the possible solutions for "x" cannot be 4 or -4 because those would end up resulting in division by zero. Transforming the equation by multiplying all terms by (x-4)(x+4) leads to this equation: (x+4) + (x-4) = 8, or 2x = 8, or x = 4. This is an extraneous solution because it is not in the original domain; as a result, the equation does not have a solution.