Algebra

Forgetting to Check for Extraneous Solutions

Students solve a transformed equation and keep every candidate answer without checking it in the original equation.

Quick check

Why students make it

They treat operations like squaring both sides or clearing denominators as if they always preserve exactly the same solutions. These steps can add values that satisfy the new equation but not the original one.

The rule done right

After any step that can change the solution set, such as squaring both sides, multiplying by a variable expression, or combining logs, substitute each candidate into the original equation. Keep only values that make the original equation true and are in the original domain.

Related resources

extraneous-solutionsradicalsrational-equations