Name ___________________________________
Advanced Algebra
CHAPTER 8
Period ______ Date _______________________
RATIONAL FUNCTIONS
Solving Rational Equations with Extraneous Solutions
2. A student solved the equation
Explain.
5
𝑥−4
=
𝑥
𝑥−4
and got as solutions 4 and 5. Which, if either, of these is extraneous?
In questions 7-8; 11-12 solve each equation by cross multiplying. Check for extraneous solutions.
In questions 20-21; 23-25 solve each equation using the LCD. Check for extraneous solutions.
In questions 26 and 27 describe and correct the error in the first step of solving the equation.
30. Patty Patriot and Goldie Hawk are going to paint the bedroom of a friend as a surprise for her birthday. They
know that by herself it would take Goldie 12 hours to complete the job. If they work together, they think it will
take them 4 hours to finish painting the room. Set up and solve an equation to fin how long Patty would take
to paint the bedroom by herself.
31. Harry Potter and Ron are going to clean Hagrid’s cabin to thank him for all the things he has done for them. If
left alone, Ron would take three hours more than Harry would by himself. If the two of them work together, it
will take them 6 hours to complete the task. Find how long it would take for each of them to clean Hagrid’s
cabin by themselves. Round your answers to the nearest tenth.
Review Questions:
Perform the indicated operation and simplify.
Advanced Algebra
ANSWER KEY
CHAPTER 8
RATIONAL FUNCTIONS
Solving Rational Equations with Extraneous Solutions
2. A student solved the equation
Explain.
5
𝑥−4
=
𝑥
𝑥−4
and got as solutions 4 and 5. Which, if either, of these is extraneous?
30. Patty Patriot and Goldie Hawk are going to paint the bedroom of a friend as a surprise for her birthday. They
know that by herself it would take Goldie 12 hours to complete the job. If they work together, they think it will
take them 4 hours to finish painting the room. Set up and solve an equation to fin how long Patty would take
to paint the bedroom by herself.
1 1
1
+
= → 𝑥 = 6: it would take Patty six hours to paint the room by herself
𝑥 12 4
31. Harry Potter and Ron are going to clean Hagrid’s cabin to thank him for all the things he has done for them. If
left alone, Ron would take three hours more than Harry would by himself. If the two of them work together, it
will take them 6 hours to complete the task. Find how long it would take for each of them to clean Hagrid’s
cabin by themselves. Round your answers to the nearest tenth.
1
1
1
9 + 3√17
+
= →ℎ=
≈ 10.7
ℎ ℎ+3 6
2
It would take Harry 10.7 hours and Ron 13.7 hours to clean Hagrid′ s cabin by themselves
Review Questions:
Perform the indicated operation and simplify.