Solutions

Extraneous Solutions

Earlier in this unit there was an explanation of excluded values. These values are important to the solution of rational equations. After solving a rational equation, be sure the solution is not an excluded value.

Example 1 This IS an extraneous solution.

The solution to is x = 1, but x = 1 is an excluded value of the original equation, so x = 1 is an extraneous solution and not a member of the solution set. This rational equation has no solution.

Example 2 This IS NOT an extraneous solution.

The solution to is x = -25. The excluded values of the original equation were , so x = -25 is a member of the solution set.