Chapter 21

RATIONAL EQUATIONS AND INEQUALITIES

The preceding chapter explored the arithmetic manipulation of rational

expressions; in this chapter, those skills are harnessed to solve rational

equations. In addition, this chapter explores direct and indirect variation,

as well as solving and graphing rational inequalities.

Make sure you’ve worked through Chapter 20 before you start this

chapter, so that you know how to add, subtract, multiply, and divide

fractions containing polynomials. You need those skills to solve equations

featuring those sorts of fractions.

This chapter also discusses variation in the form of word problems. You

describe a direct or indirect variation relationship using a rational

equation and then solve it.

Finally, this chapter explains how to solve inequalities that contain rational

expressions. Basically, you use a slightly modied version of the technique

described in Problems 14.35–14.43 for solving quadratic inequalities.

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