Q:
# 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.

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