Partial Fraction Decomposition

Many rational functions can be expressed as a sum of simpler fractions. For example, can be expressed as the sum . To find A and B, Heaviside's method can be used. First, multiply the original fraction by , cancel, and substitute 1 for : . Similarly,

. Thus, . For more complicated fractions it is best to set up and solve a linear system of equations. There are many methods for partial fraction decomposition; all of them are performed by the Mathematica function Apart.