Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 5.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominators

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rational Expressions Adding and Subtracting Rational Expressions with Common Denominators If are rational expressions, then and To add or subtract rational expressions, add or subtract numerators and place the sum or difference over the common denominator.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Add. Adding Rational Expressions Example

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Subtract: Subtracting Rational Expressions Example

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Subtract: Subtracting Rational Expressions Example

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. To add or subtract rational expressions with different denominators, you have to change them to equivalent forms that have the same denominator (a common denominator). This involves finding the least common denominator of the two original rational expressions. Least Common Denominators

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. To Find the Least Common Denominator (LCD) Step 1: Factor each denominator completely. Step 2:The least common denominator (LCD) is the product of all unique factors found in Step 1, each raised to a power equal to the greatest number of times that the factor appears in any one factored denominator. Least Common Denominators

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find the LCD of the following rational expressions. Least Common Denominators Example

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find the LCD of the following rational expressions. Least Common Denominators Example

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find the LCD of the following rational expressions. Least Common Denominators Example

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Find the LCD of the following rational expressions. Both of the denominators are already factored. Since each is the opposite of the other, you can use either x – 3 or 3 – x as the LCD. Least Common Denominators Example

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. To change rational expressions into equivalent forms, we use the principal that multiplying by 1 (or any form of 1), will give you an equivalent expression. Writing Equivalent Rational Expressions

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rewrite the rational expression as an equivalent rational expression with the given denominator. Equivalent Expressions Example