Chapter 20

RATIONAL EXPRESSIONS

The foundational methods by which a rational number is reduced to low-

est terms are used to reduce rational expressions as well. By extension, the

methods by which rational expressions are combined (that is, added, sub-

tracted, multiplied, and divided) are based on the same principles that gov-

ern the combination of rational numbers. The similarities between rational

numbers and rational expressions, however, do not preclude the need to

thoroughly investigate the latter.

Rational numbers (fractions) and rational expressions (fractions with

x in them) are a lot alike. For example, you simplify a rational expression

by factoring the numerator and denominator and then canceling out

matching factors across the fraction bar—the same way you simplify

fractions containing only numbers. Even though the processes are the same,

there are tiny differences you learn about in this chapter.

Most of this chapter is familiar. Want to add or subtract rational

expressions? You need a common denominator. Want to multiply them?

No problem; go ahead. Want to divide rational expressions? Keep the

rst fraction the same, change division to multiplication, and ip the

second fraction. Basically, you’re extending the things you learned about

fractions in Chapter 2, to include fractions with variables inside.

The chapter ends with graphing rational expressions, which is a little bit

tricky, especially the bit about oblique asymptotes, so make sure you pay

particular attention to that.

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