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The Humongous Book of Algebra Problems by W. Michael Kelley

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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, youre 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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