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 1:
Solve for , .
But 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, is an extraneous solution. So, the equation has no solutions.
Example 2:
Solve for ,
Check your solutions in the original equation.
Let .
So, is a solution.
Let .
So, is an extraneous solution.