Math 101 Intermediate Algebra

Solving Rational Equations
Chapter 7, Section 4

What is a Rational Equation?

A rational equation is an equation that contains at least one rational expression.

To Solve a Rational Equation......

  1. Determine the lowest common denominator of all rational expressions in the equation.

  2. Multiply both sides of the equation by the lowest common denominator.

  3. Simplify by removing parentheses and combining like terms.

  4. Solve the equation resulting from step 4.

  5. Check the solution in the original equation. This step is essential since it is here that you will eliminate extraneous solutions (see below).

What are Extraneous Solutions?

An extraneous solution is a value that you think is a solution because it was found by the solving process but, this value does not solve the original equation.

The way that you determine that a value is an extraneous solution is by checking that value in the original equation:

  • If a value that you think is a solution does not solve the original equation, then that value is an extraneous solution.

The check step is where extraneous solutions are found.

Always check all solutions in the original equation to make sure they solve the original equation.