Use the result of Exercise 14 to find the partial fraction decomposition of

Data from in Exercise 14

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:

x³ x4 3x² + 1 13x² + 12x