1. Under what situation would one or more solutions of a rational equation be unacceptable?
After solving a rational equation, you must always check the answers to make sure you didn't "accidentally" make a denominator equal to zero. This is not EVER allowed! Denominators must NEVER equal zero--at least not in this lifetime! These are called "EXTRANEOUS ROOTS" and they must be rejected.
For rational equations, extraneous solutions are values that cause any denominator in the original problem to be 0. Of course, when we have 0 in the denominator we have an expression that is undefined.So, we would have to discard any values that would cause the denominator to be 0.
Example: Solve for x
3 x 3