Extraneous Solutions

An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.

Example:

But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed!  .  Therefore, it cannot be a root of the original equation.  So, 2 is an extraneous solution. So, the equation has no solutions.


Example:

Check your solutions in the original equation.

         

So, 5 is a solution.                        Hence, 0 is an extraneous solution.