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Copyright © 2011 Pearson Education, Inc. Rational Expressions Section P.6 Prerequisites
P.6 Copyright © 2011 Pearson Education, Inc. Slide P-3 A rational expression is a ratio of two polynomials in which the denominator is not the zero polynomial. The domain of a rational expression is the set of all real numbers that can be used in place of the variable. Note: Rational expressions are to algebra what fractions are to arithmetic. In arithmetic we learned that each rational number has infinitely many equivalent forms. This fact is due to the basic principle of rational numbers. Basic Principle of Rational Numbers If a, b, and c are integers with b 0 and c 0, then Reducing
P.6 Copyright © 2011 Pearson Education, Inc. Slide P-4 Definition: Multiplication of Rational Numbers If a/b and c/d are rational numbers, then We multiply rational expressions in the same manner as rational numbers. Of course, any common factor can be divided out as we do when reducing rational expressions. Multiplication
P.6 Copyright © 2011 Pearson Education, Inc. Slide P-5 We divide rational numbers by multiplying by the reciprocal of the divisor, or invert and multiply. Rational expressions are divided in the same manner as rational numbers. Definition: Division of Rational Numbers If a/b and c/d are rational numbers with c 0, then Division
P.6 Copyright © 2011 Pearson Education, Inc. Slide P-6 The addition of fractions can be carried out only when their denominators are identical. To get a required denominator, we may build up the denominator of a fraction. We multiply the numerator and denominator of a fraction by the same nonzero number to get an equivalent fraction. Definition: Addition and Subtraction of Rational Numbers If a/b and c/b are rational numbers, then and Addition and Subtraction
P.6 Copyright © 2011 Pearson Education, Inc. Slide P-7 For fractions with different denominators, we build up one or both denominators to get denominators that are equal to the least common multiple (LCM) of the denominators. The least common denominator (LCD) is the smallest number that is a multiple of all of the denominators. Procedure: Finding the LCD 1. Factor each denominator completely. 2. Write a product using each factor that appears in a denominator. 3. For each factor, use the highest power of that factor that occurs in the denominators. Addition and Subtraction
Operations on Rational Expressions Review
Slide 7- 1 Copyright © 2012 Pearson Education, Inc.
Chapter 7 Section 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
The Fundamental Property of Rational Expressions
Chapter 6 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common Denominators Find the least common denominator for.
Copyright © Cengage Learning. All rights reserved.
CHAPTER 4 Fraction Notation: Addition, Subtraction, and Mixed Numerals Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.1Least Common.
Chapter 7 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiplying and Dividing Rational Expressions Multiply rational.
CHAPTER 6 Polynomials: Factoring (continued) Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 6.1Multiplying and Simplifying Rational Expressions.
Operations on Rational Expressions Digital Lesson.
Fractions Chapter Simplifying Fractions Restrictions Remember that you cannot divide by zero. You must restrict the variable by excluding any.
MATH 2A CHAPTER EIGHT POWERPOINT PRESENTATION
Adding and Subtracting Rational Expressions
Chapter 7 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common Denominators Find the least common denominator for.
Copyright © Cengage Learning. All rights reserved. Fundamentals.
6-1 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Addition, Subtraction, and Least Common Denominators Addition When Denominators Are the Same.
Rational Expressions Much of the terminology and many of the techniques for the arithmetic of fractions of real numbers carry over to algebraic fractions,
Chapter P Prerequisites: Fundamental Concepts of Algebra Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.6 Rational Expressions.
Section 1.4 Rational Expressions
Copyright © 2007 Pearson Education, Inc. Slide R-1.
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