Suppose the denominator of a rational function can be factored into distinct linear factors for a positive
Question:
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,..., Cn. If N is a polynomial of degree less than n, show that
where Pk = N(Ck)/D'(ck) 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) - . -
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