6 ­ Notes ­ Solving Rational Equations.notebook
March 31, 2017
Solving Rational Equations
A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
MCC9‐12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from simple rational functions.★
MCC9‐12.A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.★ (Limit to radical and rational functions.)
MCC9‐12.A.REI.11 Explain why the x‐coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are rational.★
Oct 24­4:15 PM
What am I learning today?
How to solve rational equations.
How will I show that I learned it?
Solve a rational equation and check for extraneous solutions.
Mar 21­4:50 PM
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6 ­ Notes ­ Solving Rational Equations.notebook
March 31, 2017
Vocabulary
Extraneous Solutions ­ Solutions that do not work in the original function because they are excluded values in the domain.
Mar 21­4:52 PM
Steps to solving rationals:
1. Determine your values that make the fractions
undefined. (exclusions of the domain)
2. Multiply each term by the least common
denominator.
**Cross-multiply if
3. Solve each problem as a polynomial.
4. Check for extraneous solutions.
(Are your solutions any of the exclusions from the
domain?!?)
Feb 2­9:45 AM
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6 ­ Notes ­ Solving Rational Equations.notebook
March 31, 2017
Example 1
Apr 14­3:43 PM
Example 2
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6 ­ Notes ­ Solving Rational Equations.notebook
March 31, 2017
Example 3
Apr 14­3:47 PM
Example 4
Mar 7 ­ 3:34 PM
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6 ­ Notes ­ Solving Rational Equations.notebook
March 31, 2017
Example 5
Mar 7 ­ 3:36 PM
Example 6
Mar 7 ­ 3:36 PM
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6 ­ Notes ­ Solving Rational Equations.notebook
March 31, 2017
Example 7
Mar 7 ­ 3:36 PM
Word problem from book p. 216 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? Is our answer reasonable?
Understanding the Problem
The answer will be the average speed of the current.
Important info:
Kayaker spent 4 hours kayaking
3 miles upstream & 3 miles downstream
Average speed in still water is 2 mi/h
Oct 24­5:54 PM
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6 ­ Notes ­ Solving Rational Equations.notebook
March 31, 2017
Make a Plan:
Let c represent the speed of the current . When the kayaker is going upstream, her speed is equal to her speed in still water minus c. When the kayaker is going down stream, her speed is equal to her speed in still water plus c.
Oct 24­6:01 PM
Work Application
p. 217
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?
Jason's rate: of the tank per hour
Lacy's rate: of the tank per hour, where h is the # of hours needed to clean the tank by herself
Oct 24­6:02 PM
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6 ­ Notes ­ Solving Rational Equations.notebook
March 31, 2017
HW: p. 219 ­ 220 # 2­10, 19 ­ 29
Oct 24­5:49 PM
Mar 31­1:42 PM
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