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Mastering Rational Expressions: Adding and Subtracting Methods

Learn how to add and subtract rational expressions with the same or different denominators. Find the LCD, combine numerators, and simplify to lowest terms. Avoid common sign errors in subtraction. Classroom examples provided.

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Mastering Rational Expressions: Adding and Subtracting Methods

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  1. Chapter 6 Section 4

  2. Adding and Subtracting Rational Expressions Add rational expressions having the same denominator. Add rational expressions having different denominators. Subtract rational expressions. 6.4 2 3

  3. Objective 1 Add rational expressions having the same denominator. Slide 6.4-3

  4. Adding Rational Expressions (Same Denominator) If and (Q ≠ 0) are rational expressions, then ADD the numerators and keep the same denominator. Add rational expressions having the same denominator. Add. Write each answer in lowest terms. Slide 6.4-4

  5. Objective 2 Add rational expressions having different denominators. Slide 6.4-6

  6. Adding Rational Expressions (Different Denominators) Step 1:Find the least common denominator (LCD). Add rational expressions having different denominators. Step 2:Rewrite each rational expressionas an equivalent rational expression with the LCD as the denominator. Step 3:Addthe numerators to get the numerator of the sum. The LCD is the denominator of the sum. Step 4:Write in lowest termsusing the fundamental property. Slide 6.4-7

  7. Add. Write each answer in lowest terms. CLASSROOM EXAMPLE 2 Adding Rational Expressions (Different Denominators) Solution: Slide 6.4-8

  8. Add. Write the answer in lowest terms. CLASSROOM EXAMPLE 3 Adding Rational Expressions Solution: Slide 6.4-9

  9. Add. Write the answer in lowest terms. CLASSROOM EXAMPLE 4 Adding Rational Expressions Solution: Slide 6.4-10

  10. Add. Write the answer in lowest terms. CLASSROOM EXAMPLE 5 Adding Rational Expressions (Denominators Are Opposites) Solution: Slide 6.4-11

  11. Objective 3 Subtract rational expressions. Slide 6.4-12

  12. Subtract. Write the answer in lowest terms. CLASSROOM EXAMPLE 6 Subtracting Rational Expressions (Same Denominator) Solution: Sign errors often occur in subtraction problems. Be sure to use parentheses after the subtraction sign. Slide 6.4-14

  13. Subtract. Write the answer in lowest terms. CLASSROOM EXAMPLE 7 Subtracting Rational Expressions (Different Denominators) Solution: Slide 6.4-15

  14. CLASSROOM EXAMPLE 9 Subtracting Rational Expressions Subtract. Write the answer in lowest terms. Solution: Slide 6.4-17

  15. Subtract. Write the answer in lowest terms. CLASSROOM EXAMPLE 8 Subtracting Rational Expressions (Denominators Are Opposites) Solution: Slide 6.4-16

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