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Mastering Partial Fraction Decomposition

Learn how to reduce rational functions using partial fraction decomposition, identify proper and improper fractions, work with quadratic and repeated factors in partial fractions, and solve problems step by step. Improve your algebra skills today!

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Mastering Partial Fraction Decomposition

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  1. Partial Fraction

  2. Partial Fractions The partial fraction decomposition or partial fraction expansion is used to reduce the degree of either the numerator or the denominator of a rational function/algebraic fraction. Proper and Improper Fraction Revisited The fraction is proper, if degree of the denominator > degree of the numerator Eg. The fraction is improper, if degree of the denominator ≤ degree of the numerator Eg.

  3. Partial Fractions with a quadratic factor Simple denominators Repeated factor

  4. Partial fraction with simple denominators: An expression in the form can be split into partial fractions of the form . Eg. Express in partial fractions. Let

  5. Let x=2, Let x= 0, So, the partial fractions are

  6. Try: • Split into partial fractions. • Split into partial fractions.

  7. Try: Answers 1 2

  8. Partial fraction with a repeated factor: An expression in the form can be split into partial fractions of the form Eg.

  9. Express in partial fractions. Solution: Let x=3, x=0, x= 1,

  10. Try: Express in partial fractions.

  11. Answer:

  12. Partial fraction with a quadratic factor: An expression in the of the form , where r and s have the same sign, can be split into partial fractions of the form Eg.

  13. Express in partial fraction. Solution: Let x = -2, x = 0, x = 1,

  14. Improper fractions: Eg. Eg. Degree of numerator = Degree of denominator: Degree of numerator > degree of denominator:

  15. Try: Decompose the following rational function into partial fractions: Answer:

  16. Further information:

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