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    Partial Fraction Decomposition Case

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    Let a1, a2,..., an be n distinct numbers and set f(x)=see attached. An identity see attached

    is called a partial fraction decomposition of f(x).
    i. Show that the preceding identity is equivalent to a nonhomogeneous system of n linear equations in the variable c1, c2,...,cn
    ii. Show that the system of homogeneous equations corresponding to the preceding identity has a unique solution, thus a unique partial fraction decomposition for f(x) is guaranteed.

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    Solution Preview

    i. Equating the expressions one has:

    Multiply both sides by :

    Each polynomial in is a polynomial of degree , with all coefficients depending on . Opening the brackets and reorganizing terms by powers of one ...

    Solution Summary

    Solution shows the working out of a special case of partial fraction decomposition is treated. Attaches a Word file.