Precalculus A Fuctional Approach to Graphing and Problem Solving

Section 4.3: Real Roots of Rational and Radical Equations

Problems 1-4
The problems called WHAT IS WRONG?, if anything, are really enhanced true/false questions. That is, simply saying "true" or "false" is not sufficient -- you need to provide reasoning as well.
Problems 5-6
These are not rational equations since there is no variable in any of the denominators, so there are no excluded values (and a check is not necessary). Multiply both sides by the least common denominator.
Problems 7-8
See Example 1.
Problems 9-10
See Example 2.
Problems 11-18
See Example 3.
Problems 19-22
See Example 5.
Problems 23-24
See Example 7.
Problems 25-28
See Example 5.
Problems 29-30
See Example 6.
Problems 31-38
See Example 3.
Problems 39-42
See Example 6.
Problems 43-44
Isolate the fourth degree term, and raise both sides to the fourth power. Don't forget to check for extraneous roots.
Problem 45
Isolate the fourth degree term, and square both sides. Isolate the radical and then square both sides again. Don't forget to check for extraneous roots.
Problems 46-52
Make substitutions as follows:
Problems 46 and 47: let w = x2
Problem 48: let w = x-2
Problem 49: let w = x-2
Problem 50: let w = (x2 - 3x)
Problem 51: let w = (x2 + 4x)
Problem 52: let w = x1/2
Problems 53-58
Multiply both sides by the least common denominator, and solve the resulting quadratic equation.

Note: Homework Hints are given only for Level 1 and Level 2 problems. Hints are generally not given for IN YOUR OWN WORDS or Journal Problems. You can also check some sources for homework help on the Links page of this web site. Don't be afraid to ask your instructor or classmates for help. You can also send an e-mail to:

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© 2011 Karl J. Smith. All rights reserved.