Mary Jane Sterling - Algebra II - 1001 Practice Problems For Dummies (+ Free Online Practice)

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115–130 Solve the quadratic inequalities.

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Chapter 3

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.

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

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

131–150 Solve the rational equations for x.

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