Theory of Intelligence
11TH•Mathematics•Partial Fractions•Exercise 5.1

Case: $(x-a)^2(x-b)^2$

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Case: (x−a)2(x−b)2(x-a)^2(x-b)^2

Include terms for each power:

P(x)(x−a)2(x−b)2=Ax−a+B(x−a)2+Cx−b+D(x−b)2\frac{P(x)}{(x-a)^2(x-b)^2}=\frac{A}{x-a}+\frac{B}{(x-a)^2}+\frac{C}{x-b}+\frac{D}{(x-b)^2}

Some coefficients may turn out to be zero.

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