8-6 Solving Rational Equations

Objectives

To solve rational equations

To use rational equations to solve problems

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Sometimes you can solve a problem using a proportion—an equation involving two rational expressions set equal to each other.

Essential Understanding To solve an equation containing rational expressions, first multiply each side by the least common denominator of the rational expressions. Doing this, however, can introduce extraneous solutions.

A rational equation contains at least one rational expression. You can simplify solving a rational equation if you first clear the equation of denominators. You can do this by multiplying by the LCD of the rational expressions in the equation.

Any time you multiply each side of an equation by an algebraic expression, it is possible to introduce an extraneous solution. Recall that an extraneous solution is a solution of the derived equation, but not a solution of the original equation. You must check all solutions in the original equation to confirm that they are indeed solutions.

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