# Partial Fraction Decomposition Case

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.

https://brainmass.com/math/linear-algebra/partial-fraction-decomposition-case-583108

#### Solution Preview

Solution:

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.