Partial Fraction Decomposition

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Partial Fraction Decomposition
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• Why do we use them?
• In Calculus, it is easier to graph and find
  limits if we split complex expressions into
  simpler expressions
• How do we create them?
• Factor the denominator
• Write separate fractions for each factor or power
  of factor
• a) If a term is raised to an exponent, you must
  write it for each power up to that exponent
• Multiply equation by LCD
• Set numerators equal and plug in a convenient
  value for x to solve for A, B, C
• Plug values for A, B, C back into separate
  fractions

3
Write the partial fraction decomposition for

• 1. Factor denominator
• 2. Split into 2 fractions
• 3. Find LCD, then set numerators equal
• 4. Plug in x-values to find A B
• 5. Rewrite decomposition with values of A B

4
Write the partial fraction decomposition for

• 1. Factor denominator
• 2. Split into 2 fractions Use part A!!
• 3. Find LCD, then set numerators equal
• 4. Plug in x-values to find A, B, C

5
Write the partial fraction decomposition for

• 5. To find B, plug in A C, then choose a value
  for x
• 6. Plug in A, B, and C into the decomposition