8.1.5 Solving Rational Equations and Inequalities Key Objectives • Solve rational equations and inequalities. Key Terms • A rational equation is an equation that contains one or more rational expressions. • An extraneous solution is a solution of a derived equation that is not a solution of the original equation. • A rational inequality is an inequality that contains one or more rational expressions. To solve a rational equation, start by multiplying each term of the equation by the least common denominator (LCD) of all of the expressions in the equation. This step eliminates the denominators of the rational expressions and results in an equation that is no longer rational. The resulting equation can be solved using algebraic techniques. Example 1 Solving Rational Equations If a rational equation has only one rational term, then the LCD is the denominator of that term.
189
Made with FlippingBook - Share PDF online