Objective: Students will be able to solve rational
equations and inequalities.
Vocabulary
 **Remember that a rational expression is a quotient of
two polynomials
 Rational equation – an equation that contains one or
more rational expressions.
 Extraneous solution – a solution of a solved equation
that is not a solution of the original equation.
 Rational inequality – an inequality that contains one or
more rational expressions.
Part 1: Solving Rational Equations
 To solve a rational equation, you must first multiply each
term of the equation by the least common denominator
(LCD) of all of the rational expressions in the equation.
 Directions: Solve the equation.
 Example 1:
Example 2 … your turn
 Solve
Example 3
 Solve
Example 4 … your turn
 Solve
Part 2: Extraneous Solutions
 Example 5: Solve
Example 6
 Solve
Example 7 … your turn
 Solve
Homework for tonight
 Homework # ____
 Textbook pg. 353 #19, 20, 22, 24, 25, 26
Problem Solving Applications
 Example 8: A kayaker spends an afternoon paddling on a
river. She travels 3 miles upstream and 3 miles 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?
Example 9
 A jet travels 3950 miles from Chicago to London, and 3950
miles back from London to Chicago. The total flying time is
16.5 hours. The return trip takes longer due to winds that
generally blow from west to east. If the jet’s average speed
with no wind is 485 mi/h, what is the average speed of the
wind during the round-trip flight? Round to the nearest mi/h.
Example 10
 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?
Example 11
 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? Round to the nearest minute.
Homework for tonight
 Homework # ______
 #1: On a different river, the kayaker travels 2 miles
upstream and 2 miles downstream in a total of 5
hours. What is the average speed of the current of
this river? Round to the nearest tenth.
 Pg. 353 # 28 & 29