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Adding and Subtracting Rational Expressions: Finding the Least Common Denominator

Learn how to add and subtract rational expressions with different denominators by finding the least common denominator (LCD) and simplifying the results in lowest terms. Practice examples included.

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Adding and Subtracting Rational Expressions: Finding the Least Common Denominator

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  1. Adding and SubtractingRational Expressions Lesson 3.10 Page 171

  2. Example 1: (Adding-Like)

  3. Example 2: (Adding-Like)

  4. Example 3: (Subtracting-Like)

  5. Example 4: (Subtracting-Like)

  6. What happens if the denominators are not the same? You must make them the same by finding a least common denominator (LCD)!

  7. Definition: LCDLeast Common Denominator The least common denominator (LCD) of two or more rational expressions is the product of the factors of the rational expressions with each common factor used only once. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140 14, 28, 42, 56, 70, 84, 98, 112, 126, 140

  8. Example 5: (Adding-Unlike)

  9. Adding or Subtracting Rational Expressions with Different Denominators • Find the least common denominator (LCD). • Rewrite each rational expression as an equivalent fraction with the least common denominator as the denominator. • Add or subtract the numerators to get the numerator sum or difference. The least common denominator is the denominator. • Write the answer in lowest terms.

  10. Example 6: (Adding-Unlike)

  11. Example 7: (Subtracting-Unlike) First factor the denominators.

  12. Rewrite each rational expression as an equivalent fraction with the least common denominator as the denominator.

  13. Subtract the numerators. The least common denominator is the denominator.

  14. Finally write the answer in lowest terms.

  15. Homework Assignment: Page 173 # 1 – 6 all # 13 – 18 all

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