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