# partial fractions

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## partial fractions

[′pär·shəl ′frak·shənz]
(mathematics)
A collection of fractions which when added are a given fraction whose numerator and denominator are usually polynomials; the partial fractions are usually constants or linear polynomials divided by factors of the denominator of the given fraction.
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In extreme cases, it is the sum of partial fractions or a continued fraction of the analyzed dynamic characteristic [Y.
U](s) is decomposed into partial fractions, obtaining
Next substituting u = 1 and using partial fractions we obtain
Together with some elementary facts of linear algebra, we finally arrive at a first inversion algorithm which requires the computation of the partial fraction decomposition of [(det([lambda]I - A)).
It is well known that the coefficients in the partial fraction decomposition can be computed by means of an ansatz and the solution of a corresponding linear system of equations.
Chapter 8: When All Else Fails: Integration with Partial Fractions.

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