Adding and Subtracting Rational Expressions 1 2 3

Adding and Subtracting Rational Expressions 1 2 3 Add rational expressions having the same denominator. Add rational expressions having different denominators. Subtract rational expressions. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Objective 1 Add rational expressions having the same denominator. Copyright © 2008 Pearson Education,

Add rational expressions having the same denominator. We find the sum of two rational expressions with the same procedure that we used in Section 1. 1 for adding two fractions having the same denominator. If and (Q ≠ 0) are rational expressions, then That is, to add rational expressions with the same denominator, add the numerators and keep the same denominator. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 3

EXAMPLE 1 Adding Rational Expressions with the Same Denominator Add. Write each answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 4

Objective 2 Add rational expressions having different denominators. Copyright © 2008 Pearson Education, Inc.

Add rational expressions having different denominators. We use the following steps, which are the same as those used in Section 1. 1 to add fractions having different denominators. Step 1: Find the least common denominator (LCD). Step 2: Rewrite each rational expression as an equivalent rational expression with the LCD as the denominator. Step 3: Add the numerators to get the numerator of the sum. The LCD is the denominator of the sum. Step 4: Write in lowest terms using the fundamental property. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 6

EXAMPLE 2 Adding Rational Expressions with Different Denominators Add. Write each answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 7

EXAMPLE 3 Adding Rational Expressions Add. Write the answer in lowest terms. Solution: Copyright

EXAMPLE 4 Adding Rational Expressions Add. Write the answer in lowest terms. Solution: Copyright

EXAMPLE 5 Adding Rational Expressions with Denominators That Are Opposites Add. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 10

Objective 3 Subtract rational expressions. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson

Subtract rational expressions. Use the following rule to subtract rational expressions having the same denominator. If and (Q ≠ 0) are rational expressions, then That is, to subtract rational expressions with the same denominator, subtract the numerators and keep the same denominator. We subtract rational expressions having different denominators using a procedure similar to the one used to add rational expressions having different denominators. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 12

EXAMPLE 6 Subtracting Rational Expressions with the Same Denominator Subtract. Write the answer in lowest terms. Solution: Sign errors often occur in subtraction problems. The numerator of the fraction being subtracted must be treated as a single quantity. Be sure to use parentheses after the subtraction sign. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 13

EXAMPLE 7 Subtracting Rational Expressions with Different Denominators Subtract. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 14

EXAMPLE 8 Subtracting Rational Expressions with Denominators That Are Opposite Subtract. Write the answer in lowest terms. Solution: Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7. 4 - 15