Partial fraction decomposition

Lessons

• Introduction
  Introduction to Partial Fraction Decomposition
  a)

  What is partial fraction decomposition?
  
  
  b)

  When can we perform partial fraction decomposition?
  
  

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• 1.
  Case 1: Denominator is a product of linear factors with no repeats

  Find the partial fractions of:

  a)

  $\frac{x + 7}{(x + 3)(x - 1)}$
  
  
  b)

  $\frac{4x + 3}{x^{2} + x}$
  
  

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• 2.
  Case 2: Denominator is a product of linear factors with repeats

  Find the partial fractions of :

  a)

  $\frac{3x^{2} - 5}{(x - 2)^{3}}$
  
  
  b)

  $\frac{2x - 1}{x^{2} + 10x + 25}$
  
  

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• 3.
  Case 3: Denominator contains irreducible quadratic factors with no repeats

  Find the partial fractions of :

  $\frac{2x^{2} + 5x + 8}{x^{3} - 8x}$

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• 4.
  Case 4: Denominator contains irreducible quadratic factors with repeats

  Find the partial fractions of:

  $\frac{3x^{4} + x^{3} + 1}{x(x^{2} + 1)^{2}}$

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• 5.
  First perform long division, then partial fraction decomposition

  Find the partial fractions of:

  a)

  $\frac{x^{3} - 3x^{2} + 4x}{x^{2} - 3x 2}$
  
  
  b)

  $\frac{2x^{2} + 14x + 24}{x^{2} + 6x - 16}$
  
  

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