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

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

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

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.

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

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

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

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

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

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.

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:

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

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