Example:
This suggests two solutions,
and 
.
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because
is defined only for 
(assuming you're looking for real solutions only). So, we call an extraneous solution, and the complete solution set (over the real numbers) is .
This suggests two solutions,
However, upon plugging these solutions back into the equation, you get
which checks out, but
does not because