The Method of Partial Fractions

4. The denominator has a repeated linear factor; so we use the setup

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Note that the least common denominator for this problem is tex2html_wrap_inline619. Here is the final answer:

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Some fine points.

(1) All examples so far have dealt with fractions, where the degree of the numerator is less than the degree of the denominator. For good reason: If the degree on top is at least as big as the degree on the bottom, one can first perform polynomial division, and then apply the method of partial fractions to the remainder term:

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and then use tex2html_wrap_inline625 to obtain

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Try it yourself!

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Helmut Knaust
Fri Jul 5 13:54:22 MDT 1996

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