Ilim ha’m ja’miyet № 3-1 (2026) · Саҳифаҳои 17-20

RATIONAL FRACTIONS AND METHODS FOR DECOMPOSING THEM INTO UNIT FRACTIONS

Kalekeeva, Tamara Turkmenbaevna, Utepbergenova, Aymereke Dauletmuratovna, Kuanyshbaeva, Khurliman Sabitovna, Kalekeeva, Tamara Turkmenbaevna, Utepbergenova, Aymereke Dauletmurat qızı, Quanıshbaeva, Hurliman Sabit qızı, Калекеева, Тамара Туркменбаевна, Утепбергенова, Аймереке Даулетмуратовна, Куанышбаева, Хурлиман Сабитовна

Дар манбаъ хондан

Аннотатсия

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.

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Иқтибос гирифтан

APA 7 
Kalekeeva, Tamara Turkmenbaevna, Utepbergenova, Aymereke Dauletmuratovna, Kuanyshbaeva, Khurliman Sabitovna, Kalekeeva, Tamara Turkmenbaevna, Utepbergenova, Aymereke Dauletmurat qızı, Quanıshbaeva, Hurliman Sabit qızı, Калекеева, Тамара Туркменбаевна, Утепбергенова, Аймереке Даулетмуратовна & Куанышбаева, Хурлиман Сабитовна (2026). RATIONAL FRACTIONS AND METHODS FOR DECOMPOSING THEM INTO UNIT FRACTIONS. Ilim ha’m ja’miyet, (3-1), 17-20.
GOST R 7.0.5 
Kalekeeva, Tamara Turkmenbaevna, Utepbergenova, Aymereke Dauletmuratovna, Kuanyshbaeva, Khurliman Sabitovna, Kalekeeva, Tamara Turkmenbaevna, Utepbergenova, Aymereke Dauletmurat qızı, Quanıshbaeva, Hurliman Sabit qızı, Калекеева, Тамара Туркменбаевна, Утепбергенова, Аймереке Даулетмуратовна, Куанышбаева, Хурлиман Сабитовна RATIONAL FRACTIONS AND METHODS FOR DECOMPOSING THEM INTO UNIT FRACTIONS // Ilim ha’m ja’miyet. 2026. № 3-1. С. 17-20.
BibTeX 
@article{turkmenbaevna2026,
  author  = {Kalekeeva, Tamara Turkmenbaevna and Utepbergenova, Aymereke Dauletmuratovna and Kuanyshbaeva, Khurliman Sabitovna and Kalekeeva, Tamara Turkmenbaevna and Utepbergenova, Aymereke Dauletmurat qızı and Quanıshbaeva, Hurliman Sabit qızı and Калекеева, Тамара Туркменбаевна and Утепбергенова, Аймереке Даулетмуратовна and Куанышбаева, Хурлиман Сабитовна},
  title   = {RATIONAL FRACTIONS AND METHODS FOR DECOMPOSING THEM INTO UNIT FRACTIONS},
  journal = {Ilim ha’m ja’miyet},
  year    = {2026},
  number  = {3-1},
  pages   = {17-20}
}
RIS 
TY  - JOUR
AU  - Kalekeeva, Tamara Turkmenbaevna
AU  - Utepbergenova, Aymereke Dauletmuratovna
AU  - Kuanyshbaeva, Khurliman Sabitovna
AU  - Kalekeeva, Tamara Turkmenbaevna
AU  - Utepbergenova, Aymereke Dauletmurat qızı
AU  - Quanıshbaeva, Hurliman Sabit qızı
AU  - Калекеева, Тамара Туркменбаевна
AU  - Утепбергенова, Аймереке Даулетмуратовна
AU  - Куанышбаева, Хурлиман Сабитовна
TI  - RATIONAL FRACTIONS AND METHODS FOR DECOMPOSING THEM INTO UNIT FRACTIONS
JO  - Ilim ha’m ja’miyet
PY  - 2026
IS  - 3-1
SP  - 17
EP  - 20
ER  -