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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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Solving Radical Equations with Multiple Radical Terms

181–190 Solve the radical equations involving two or more radical terms.

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