Chapter 3
Solving Radical and Rational Equations
A radical equation is one that starts out with a square root, cube root, or some other root and gets changed into another form to make the solving process easier. The new form may have solutions that don’t work in the original equation, but this method is still the easiest. A rational equation is one that involves a fractional expression — usually with a polynomial in the numerator and denominator. These equations are also changed in order to solve them, and they also carry the concern of an extraneous or false root.
The Problems You’ll Work On
In this chapter, you’ll work with radical and rational equations in the following ways:
Solving radical equations with just one radical term
Solving radical equations with two or more radical terms
Checking answers for extraneous roots
Solving rational equations by forming proportions
Solving rational equations by finding a common denominator
What to Watch Out For
Don’t let common mistakes like the following ones trip you up when working with radical or rational equations:
Forgetting to check for extraneous solutions
Squaring a binomial incorrectly when squaring both sides to get rid of the radical
Distributing incorrectly when writing equivalent fractions using a common denominator
Eliminating solutions that create a 0 in the denominator
Solving Rational Equations
131–150 Solve the rational equations for x.
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Taking on Radical Equations Involving One Radical Term
151–180 Solve the radical equations.
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