Educator

Rational Equations

• A rational equation is an equation that contains rational expressions.

• To solve a rational equation, multiply each term on both sides by the LCM of all the denominators in the equation. Then solve the resulting equation, which has no fractions.

• An extraneous solution is a value that makes one or more of the denominators in the original equation equal to 0. Always check all potential solutions in the original equation. Exclude extraneous values from the solution set.

• Here is a better way to deal with extraneous solutions: before solving the equation, determine the values that must be excluded by setting each denominator equal to 0 and solving. Then you will recognize an extraneous solution as soon as it appears as a possible solution.