Partial Fraction Decomposition by Division
Sidney H. L. Kung · College Mathematics Journal · 2006
In this note, we present a method for the partial fraction decomposition of two algebraic functions: (i) fix)/iax + b)1 and (\i)fix)/ipx2 + qx + r) where fix) is a polynomial of degree n, t is a positive integer, and px2 + qx + r is an irreducible (g2 < 4pr) quadratic polynomial. Our algorithm is relatively simple in comparison with those given elsewhere [1, 2, 3, 4, 5, 6, 7, 8]. The essence of the method is to use repeated division to re-express the numerator polynomial in powers of the normalized denominator. Then upon further divisions, we obtain a sum of partial fractions in the form Ai/iax 4b)1 or iBjX + Cj)/ipx2 + qx + r)j for the original function. For (i), we let c = b/a, and express fix) as follows: