Download presentation

Presentation is loading. Please wait.

Published byJuliet Francis Modified over 5 years ago

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

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google