PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. CHAPTER 7 Rational Expressions and Equations Imagine you and a friend have partnered in a business venture. You have opened a computer service shop in a local mall. The profits are good, but they seem to vary depending on how much advertising you do for the business. Do you 7.1 Simplifying Rational Expressions 431 7.2 Multiplying and Dividing Rational Expressions 437 7.3 Adding and Subtracting Rational Expressions 442 How Am I Doing? Sections 7.1–7.3 450 7.4 Simplifying Complex Rational Expressions 451 7.5 Solving Equations Involving Rational Expressions 457 7.6 Ratio, Proportion, and Other Applied Problems 462 Use Math to Save Money 470 Chapter 7 Organizer 471 Chapter 7 Review Problems 472 How Am I Doing? Chapter 7 Test 476 Math Coach 477 430431 7.1 Simplifying Rational Expressions Student Learning Objective After studying this section, you will be able to: Simplify rational expressions by factoring. Recall that a rational number is a number that can be written as one integer divided by another integer, such as 3 ÷ 4 or . We usually use the word fraction to mean . We can extend this idea to algebraic expressions. A rational exp The last fraction is sometimes also called a fractional algebraic expression. There is a special restriction for all fractions, including fractional algebraic expressions: The denominator of the fraction cannot be 0. For example, in the ex the denominator cannot be 0. Therefore, the value of x cannot be − 4. The following important restriction will apply throughout this chapter. We state it here to avoid having to mention it repeatedly throughout this chapter. RESTRICTION The denominator of a rational expression cannot be zero. Any value of the variable that would make the denominator zero is not allowed. We have discovered that fractions can be simplified (or reduced) in the following way. This is sometimes referred to as the basic rule of fractions and can be stated as follows. BASIC RULE OF FRACTIONS For any rational expression and any polynomials a, b , and c (where b ≠ 0 and c ≠ 0), We will examine several examples where a, b , and c are real numbers, as well as more involved examples where a, b , and c are polynomials. In either case we shall make extensive use of our factoring skills in this section. One essential property is revealed by the basic rule of fractions: If the numerator and denominator of a given fraction are multiplied by the same nonzero quantity, an equivalent fraction is obtained. The rule can be used two ways. You EXAMPLE 1 Page 1 of 35 Print | Beginning & Intermediate Algebra 1/31/2014 ...
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