RATIONAL FRACTIONS AND METHODS FOR DECOMPOSING THEM INTO UNIT FRACTIONS - Kalekeeva, Tamara Turkmenbaevna; Utepbergenova, Aymereke Dauletmuratovna; Kuanyshbaeva, Khurliman Sabitovna (SCIENCE and SOCIETY, 2026)
This article examines rational fractions defined over the field of real and complex numbers, their properties, and methods for factoring into sums of partial fractions. The paper presents a theory for extracting the integer part from an improper rational fraction, as well as the factorization of proper rational fractions into partial fractions using linear and quadratic factors. It also demonstrates solutions to practical examples using the method of undetermined coefficients, the Lagrange method, and Horner's scheme, and proves the main theorems. This article is intended for use as a resource for students at higher education institutions and academic lyceums.
Keywords: rational fraction; proper and improper fractions; unit fractions; factorization; Lagrange's method; Horner's scheme; complex numbers