1. Copyright © 2007 Pearson Education, Inc. Slide R-1

2. Copyright © 2007 Pearson Education, Inc. Slide R-2 Chapter R: Reference: Basic Algebraic Concepts R.1Review of Exponents and Polynomials R.2Review of Factoring R.3Review of Rational Expressions R.4Review of Negative and Rational Exponents R.5Review of Radicals

3. Copyright © 2007 Pearson Education, Inc. Slide R-3 R.3 Review of Rational Expressions A rational expression is an expression that is the quotient of two polynomials. Examples include

4. Copyright © 2007 Pearson Education, Inc. Slide R-4 R.3 Domain of a Rational Expression The domain of a rational expression is the set of real numbers for which the expression is defined. The domain consists of all real numbers except those that make the denominator 0.

5. Copyright © 2007 Pearson Education, Inc. Slide R-5 R.3 Domain of a Rational Expression For example, to find the domain of solve as follows, or The domain is

6. Copyright © 2007 Pearson Education, Inc. Slide R-6 R.3 Lowest Terms of a Rational Expression Fundamental Principle of Fractions

7. Copyright © 2007 Pearson Education, Inc. Slide R-7 R.3 Writing Rational Expressions in Lowest Terms Example Write each rational expression in lowest terms. (a)(b) Solution (a) by the fundamental principle, provided p is not 0 or –4.

8. Copyright © 2007 Pearson Education, Inc. Slide R-8 R.3 Writing Rational Expressions in Lowest Terms Solution (b) by the fundamental principle.

9. Copyright © 2007 Pearson Education, Inc. Slide R-9 R.3 Multiplying and Dividing Rational Expressions Multiplying and Dividing Fractions For fractions and and

10. Copyright © 2007 Pearson Education, Inc. Slide R-10 R.3 Multiplying and Dividing Rational Expressions Example Multiply or divide as indicated. (a)(b) Solution (a)

11. Copyright © 2007 Pearson Education, Inc. Slide R-11 R.3 Multiplying and Dividing Rational Expressions Solution (b)

12. Copyright © 2007 Pearson Education, Inc. Slide R-12 R.3 Adding and Subtracting Rational Expressions Adding and Subtracting Fractions For fractions and and Addition and subtraction are typically performed using the least common denominator.

13. Copyright © 2007 Pearson Education, Inc. Slide R-13 R.3 Adding and Subtracting Rational Expressions Finding the Least Common Denominator (LCD) 1.Write each denominator as a product of prime factors. 2.Form a product of all the different prime factors. Each factor should have as exponent the greatest exponent that appears on that factor.

14. Copyright © 2007 Pearson Education, Inc. Slide R-14 R.3 Adding and Subtracting Rational Expressions Example Add or subtract, as indicated. (a)(b) Solution (a) Write each denominator as a product of prime factors

15. Copyright © 2007 Pearson Education, Inc. Slide R-15 R.3 Adding and Subtracting Rational Expressions Solution (a) The prime factors are 2, 3 and x having greatest exponents 1, 2 and 2 respectively. The LCD is Then

16. Copyright © 2007 Pearson Education, Inc. Slide R-16 R.3 Adding and Subtracting Rational Expressions Solution (b)

17. Copyright © 2007 Pearson Education, Inc. Slide R-17 R.3 Complex Fractions A complex fraction is any quotient of two rational expressions.

18. Copyright © 2007 Pearson Education, Inc. Slide R-18 R.3 Simplifying Complex Fractions Example Simplify Solution Multiply both numerator and denominator by the LCD of all the fractions a(a + 1).

19. Copyright © 2007 Pearson Education, Inc. Slide R-19 R.3 Simplifying Complex Fractions Solution