This concept covers the general theory of partial fraction decomposition: any rational function (proper, with numerator degree less than denominator degree) can be rewritten as a sum of simpler terms determined by the factorization of the denominator, with distinct linear factors producing single constant-over-factor terms, repeated linear factors producing a term for each power up to the multiplicity, and irreducible quadratic factors producing linear-numerator terms (also repeated by power if the quadratic recurs). It relies on polynomial long division to first reduce an improper rational function, on complete factorization of the denominator (including distinguishing genuinely irreducible quadratics from quadratics that disguise a product of linear factors), and on coefficient-determination methods (the cover-up/Heaviside method, substitution of convenient values, and matching coefficients of equal polynomials). This belongs to single-variable calculus and algebra, within the theory of rational function integration, serving as the algebraic preprocessing step that reduces a rational integral to a sum of elementary integrable forms (polynomials, logarithms, arctangents).
This concept covers the general theory of partial fraction decomposition: any rational function (proper, with numerator degree less than denominator degree) can be rewritten as a sum of simpler terms…