The algebraic technique of partial fraction decomposition typically appears first in the integral calculus course as part of the methodology of integrating rational functions; and second, in any course such as differential equations where Laplace transforms must be inverted. If the Laplace transform is used in an engineering course, partial fraction decompositions must generally be implemented over the complex field so that all factors are linear. This column describes how to obtain the partial fraction decomposition in Maple, either with irreducible quadratic factors or with strictly linear factors. We also suggest some pedagogic devices for providing insight into the algebraic processes involved.