Suppose the denominator of a rational function can be factored into distinct linear factors

for a positive integer n and distinct real numbers C₁, C₂,..., C_n. If N is a polynomial of degree less than n, show that

where P_k = N(C_k)/D'(c_k) for k = 1, 2,..., n. Note that this
is the partial fraction decomposition of N(x)/D(x).

Transcribed Image Text:

- D(x) = (x − c₁)(x − c₂)⋅ ⋅ ⋅ (x − c₁) - . -