A New Approach to Partial Fractions

Algebra courses give instruction for adding or subtracting two rational functions, or ratios of polynomials. One way to do this is to find a common denominator, rewrite each rational function using this common denominator, add or subtract the numerators and simplify the result. In integral calculus, it is often necessary to reverse this process; that is, to rewrite a given rational function as a sum of several simpler rational functions, or partial fractions (see, for instance, Stewart 2001, 405-7).