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Lesson 6 Contents. Example 1 Solve a Rational Equation Example 2 Elimination of a Possible Solution Example 3 Work Problem Example 4 Rate Problem Example 5 Solve a Rational Inequality. SolveCheck your solution. The LCD for the three denominators is. Original equation. - PowerPoint PPT Presentation
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Example 1 Solve a Rational EquationExample 2 Elimination of a Possible SolutionExample 3 Work ProblemExample 4 Rate ProblemExample 5 Solve a Rational Inequality
Solve Check your solution.
The LCD for the three denominators is
Original equation
Multiply each side
by 24(3 – x).
1 1
11 1
6
Simplify.
Simplify.
Add.
Check Original equation
Simplify.
Simplify.
The solution is correct.
Answer: The solution is –45.
Answer:
Solve
Solve Check your solution.
The LCD is
Original equation
Multiply by the
LCD, (p2 – 1).
p – 1
1
1
1
DistributiveProperty
Simplify.
Simplify.
Add(2p2 – 2p + 1)to each side.
Factor.
orZero ProductProperty
Solve eachequation.
Divide eachside by 3.
Check Original equation
Simplify.
Simplify.
Since p = –1 results in a zero in the denominator, eliminate –1.
Answer: The solution is p = 2.
Simplify.
Original equation
Answer:
Solve
Mowing Lawns Tim and Ashley mow lawns together. Tim working alone could complete the job in 4.5 hours, and Ashley could complete it alone in 3.7 hours. How long does it take to complete the job when they work together?
In 1 hour, Tim could complete of the job.
In 1 hour, Ashley could complete of the job.
In t hours, Tim could complete or of the job.
In t hours, Ashley could complete or of the job.
Part completedby Tim plus
part completedby Ashley equals entire job.
1
Solve the equation.
Original equation
Multiply eachside by 16.65.
DistributiveProperty
Simplify.
Simplify.
Divide each side by 8.2.
Answer: It would take them about 2 hours working together.
Cleaning Libby and Nate clean together. Nate working alone could complete the job in 3 hours, and Libby could complete it alone in 5 hours. How long does it take to complete the job when they work together?
Answer: about 2 hours
Swimming Janine swims for 5 hours in a stream that has a current of 1 mile per hour. She leaves her dock and swims upstream for 2 miles and then back to her dock. What is her swimming speed in still water?
Words The formula that relates distance, time,
and rate is
Variables Let r be her speed in still water. Then her speed with the current is r + 1 and her speed against the current is r – 1.
Time going withthe current plus
time going againstthe current equals
totaltime.
5Equation
Solve the equation.
Originalequation
Multiply each
side by r2 – 1.
DistributiveProperty
r + 1 r – 1
1 1
Simplify.
Simplify.
Subtract 4r from each side.
Use the Quadratic Formula to solve for r.
Quadratic Formula
x = r, a = 5, b = –4, and c = –5
Simplify.
Simplify.
Use a calculator.
Answer: Since the speed must be positive, the answer is about 1.5 miles per hour.
Swimming Lynne swims for 1 hour in a stream that has a current of 2 miles per hour. She leaves her dock and swims upstream for 3 miles and then back to her dock. What is her swimming speed in still water?
Answer: about 6.6 mph
Solve
Step 1 Values that make the denominator equal to 0 are excluded from the denominator. For this inequality the excluded value is 0.
Step 2 Solve the related equation.
Related equation
Multiply each side by 9s.
Simplify.
Add.
Divide each side by 6.
Step 3 Draw vertical lines at the excluded value and at the solution to separate the number line into regions.
Now test a sample value in each region to determine if the values in the region satisfy the inequality.
Test
is a solution.
is not a solution.
Test
is a solution.
Test
Answer: The solution
Solve
Answer:
