Download presentation

Presentation is loading. Please wait.

Published byOwen Maxwell Modified over 7 years ago

2
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 12 Rational Expressions

3
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 5.1 Simplifying Rational Expressions

4
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rational Expression A rational expression is an expression that can be written in the form where P and Q are both polynomials and Q ≠ 0. Examples of Rational Expressions

5
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. To evaluate a rational expression for a particular value(s), substitute the replacement value(s) into the rational expression and simplify the result. Evaluating Rational Expressions Example Evaluate the following expression for y = 2.

6
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. In the previous example, what would happen if we tried to evaluate the rational expression for y = 5? Since division by 0 is undefined, this expression is undefined when y = 5. Evaluating Rational Expressions

7
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. To find values for which a rational expression is undefined, find values for which the denominator is 0. Undefined Rational Expressions

8
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find any values that make the following rational expression undefined. The expression is undefined when 15x + 45 = 0. So, the expression is undefined when x = 3. Undefined Rational Expressions Example

9
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Simplifying a rational expression means writing it in lowest terms or simplest form. To do this, we need to use the Fundamental Principle of Rational Expressions If P, Q, and R are polynomials, and Q and R are not 0, Simplifying Rational Expressions

10
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. To Simplify a Rational Expression Step 1:Completely factor the numerator and denominator. Step 2:Divide out factors common to the numerator and denominator. (This is the same as “removing a factor of 1.”) Simplifying Rational Expressions

11
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Helpful Hint When simplifying a rational expression, we look for common factors, not common terms.

12
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. x 2 + 5x Simplifying Rational Expressions Example 7x + 35 Simplify:

13
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Simplify: Simplifying Rational Expressions Example x 2 – x – 20 x 2 + 3x – 4

14
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Simplify: Simplifying Rational Expressions Example y – 7 7 – y

Similar presentations

© 2022 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