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

Case: $(x-a)(x-b)(x-c)$

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Case: (x−a)(x−b)(x−c)(x-a)(x-b)(x-c)

If the denominator factors into distinct linear factors, use:

P(x)(x−a)(x−b)(x−c)=Ax−a+Bx−b+Cx−c\frac{P(x)}{(x-a)(x-b)(x-c)}=\frac{A}{x-a}+\frac{B}{x-b}+\frac{C}{x-c}

Find constants by clearing denominators and substituting x=a,b,cx=a,b,c (or comparing coefficients).

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