What is an extraneous solution and in what cases do you get one?

How do you know it is extraneous?

I have a teacher asking this for College Algebra

Paul

Two of the definitions of extraneous I found in a dictionary are "not belonging or proper" and "existing or originating outside or beyond". Extraneous solutions are not solutions at all. They arise from outside the problem, from the method of solution. They are extraneous because they are not solutions of the original problem. This answers your second question. To tell if a "solution" is extraneous you need to go back to the original problem and check to see if it is actually a solution.

One example might be

Here is another example.

These are two ways that extraneous solutions can arise, division by zero and squaring both sides of an equation. They can arise also because of physical constraints. A standard math/physics problem is