Partial Fraction (Decomposition). Partial Fraction Decomposition of f(x)/d(x). Degree of f ≥ degree of d: Use the division algorithm to divide f by d to obtain the quotient q and remainder r and write f(x) = q(x) + r(x) d(x) d(x)
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A1 + A2 + … + Au , mx + n (mx + n)2 (mx + n)u
where A1, A2, …, Au are real numbers.
B1x + C1 + B2x + C2 + … + Bvx + Cv ax2 + bx + c (ax2 + bx + c)2 (ax2+bx+c)v
where B1, B2,…, Bv and C1, C2,…, Cv are real numbers. The partial fraction decomposition of the original rational function is the sum of q(x) and the fraction is the sum of q(x) and the fractions in parts 3 and 4