Notes 5­5 Solving Rational Equations and Inequalities
Objectives:
­ Solve rational equations and inequalities
Who uses this?
Kayakers can use rational equations to determine how fast a river is moving. 1
A rational equation is an equation 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 of all the expressions in the equation.
Ex. Solve. 2
Try These:
Ex. Solve each equation.
a.
b.
c. 3
An extraneous solution is a solution of an equation derived from an original equation that is not a solution of the original equation. Ex. Solve
4
b. 5
Try These:
Ex. Solve each equation
a.
b. 6
Ex. A kayaker spends an afternoon paddling on a river. She travels 3 mi upstream and 3 mi downstream in a total of 4 hours. In still water, the kayaker can travel at an average speed of 2 mi/h. Based on this information, what is the average speed of the river's current? Is your answer reasonable?
7
Try These:
Ex. On a different river, the kayaker travels 2 mi upstream and 2 mi downstream in a total of 5 hours. What is the average speed of the current of this river? Round to the nearest tenth.
8
Ex. Jason can clean a large tank at an aquarium in about 6 hours. When Jason and Lacy work together, they can clean the tank in about 3.5 hours. About how long would it take Lacy to clean the tank if she works by herself?
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Try These:
Ex. Julien can mulch a garden in 20 minutes. Together, Julien and Remy can mulch the same garden in 11 minutes. How long will it take Remy to mulch the garden when working alone?
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A rational inequality is an inequality that contains one or more rational expressions. Ex. Solve by using a graph and a table. Try these:
a.
b. 11
Ex. Solving the inequality algebraically. Check your answer for reasonableness.
Case 1 LCD is positive
Case 2 LCD is negative
12
Try These:
Solve each inequality algebraically.
a.
b. 13