(In the latter type, ax^2+bx+c is a quadratic expression which does not factorize without containing surds or imaginary terms.) Resolving an algebraic expression into partial fractions is used as a preliminary to integrating certain functions and in determining inverse Laplace transforms There are basically three types of partial fraction and the form of partial fraction used, where f (x) is assumed to be of less degree than the relevant denominator and A, B and C are constants to be determined. When the degree of the numerator is equal to or higher than the degree of the denominator, the numerator must be divided by the denominator until the remainder is of less degree than the denominator.
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