Adding and Subtracting Rational Expressions

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Adding and SubtractingRational Expressions

• Lesson 3.10
• Page 171

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Example 1 (Adding-Like)
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Example 2 (Adding-Like)
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Example 3 (Subtracting-Like)
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Example 4 (Subtracting-Like)
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What happens if the denominators are not the same?

• You must make them the same by finding a least
  common denominator!

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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
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Example 5 (Adding-Unlike)
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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.

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Example 6 (Adding-Unlike)
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Example 7 (Subtracting-Unlike)
First factor the denominators.
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Rewrite each rational expression as an equivalent
fraction with the least common denominator as the
denominator.
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Subtract the numerators. The least common
denominator is the denominator.
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Finally write the answer in lowest terms.
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HW 198 1-13 odd, 17-29 odd
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HW 198 1-13 odd, 17-29 odd