1. Section 5: Solving Rational Equations and Inequalities

2. SSolve rational equations and inequalities.

3. rrational equation eextraneous solution rrational inequality

4. KKayakers can use rational equations to determine how fast a river is moving. ((See Example 3.)

5. AA rational equation is an equation that contains one or more rational expressions. TThe time t in hours that it takes to travel d miles can be determined by using the equation t = d/r, where r is the average rate of speed. TThis equation is a rational equation.

6. T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. TThis step eliminates the denominators of the rational expressions and results in an equation you can solve by using algebra.

8. AAn extraneous solution is a solution of an equation derived from an original equation that is not a solution of the original equation. WWhen you solve a rational equation, it is possible to get extraneous solutions. TThese values should be eliminated from the solution set. AAlways check your solutions by substituting them into the original equation.

14. AA rational inequality is an inequality that contains one or more rational expressions. OOne way to solve rational inequalities is by using graphs and tables.

16. YYou can also solve rational inequalities algebraically. YYou start by multiplying each term by the least common denominator (LCD) of all the expressions in the inequality. HHowever, you must consider two cases: the LCD is positive or the LCD is negative.

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