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Partial Fractions

Partial Fractions. Idea behind partial fraction decomposition. Suppose we have the following expression Each of the two fractions on the right is called a partial fraction . The sum of these fractions I called the partial fraction decomposition of the rational expression on the left hand side.

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Partial Fractions

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  1. Partial Fractions

  2. Idea behind partial fraction decomposition • Suppose we have the following expression • Each of the two fractions on the right is called a partial fraction. The sum of these fractions I called the partial fraction decomposition of the rational expression on the left hand side.

  3. Note • The rational expression of the form . • P and Q have no common factors. • The highest power in the numerator is less than the highest power in the denominator.

  4. Case I • The partial fraction decomposition of a rational expression with distinct linear factors in the denominator.

  5. Example • Find the partial fraction decomposition of

  6. Case II • Partial fraction decomposition with repeated linear factors.

  7. Example • Find the partial fraction decomposition of

  8. Case III • The partial fraction decomposition of a rational expression with prime, nonrepeated quadratic factors in the denominator. • Suppose the factor in the denominator cannot be factored in to linear factors with real coefficients. • Under these conditions the partial fraction decomposition will contain a term of the form

  9. Example • Find the partial fraction decomposition of

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