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

Ilim ha’m ja’miyet · 2026-yil

Annotatsiya

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.

Maqolaning asl sahifasi

Kalit so‘zlar

ratsional kasr, to‘g‘ri va noto‘g‘ri kasrlar, sodda kasrlar, ko‘paytuvchilarga ajratish, Lagranj metodi, Gorner sxemasi, kompleks sonlar, рациональная дробь, правильные и неправильные дроби, простейшие дроби, разложение на множители, метод Лагранжа, схема Горнера, комплексные числа, rational fraction, proper and improper fractions, unit fractions, factorization, Lagrange's method, Horner's scheme, complex numbers

Iqtibos keltirish

@article{kalekeevatamaraturkmenbaevna2026,
  title = {RATIONAL FRACTIONS AND METHODS FOR DECOMPOSING THEM INTO UNIT FRACTIONS},
  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},
  journal = {Ilim ha’m ja’miyet},
  year = {2026},
  number = {3-1},
  pages = {17-20},
  url = {https://journal.ndpi.uz/index/article/view/2026-3-1-005}
}

Boshqa maqola uchun iqtibos tayyorlash

Ilim ha’m ja’miyet jurnalidan boshqa maqolalar

• The issue of emotional burnout among specialists working with intellectually disabled students in psychological literature

  Jumaniyozova, Nasiba Ramatillayevna, Жуманиязова, Насиба Раматиллаевна, Jumaniyozova, Nasiba Ramatillayevna · Ilim ha’m ja’miyet · 2026-04-01

  This article presents theoretical information based on scientific research in psychological sources concerning the states of emotional stress experienced by specialists working with students with intellectual…

• Research on the dynamics of composite working bodies of cotton cleaning machines and analysis of conducted studies

  Abduvaxidov, Mutaxxirxon Muboshirovich, Абдувахидов, Мутаххирхон Мубоширович, Abduvaxidov, Mutaxxirxon Muboshirovich · Ilim ha’m ja’miyet · 2026-05-16

  This paper presents an analysis of studies devoted to the dynamics of composite working bodies of cotton cleaning machines. Existing theoretical and experimental studies on the processes of bending and torsional…

• Formal methods for determining semantic similarity in natural language processing

  Abdullayev, Elmurod Zaylobidinovich, Абдуллаев, Элмурод Зайлобидинович, Abdullayev, Elmurod Zaylobidinovich · Ilim ha’m ja’miyet · 2026-05-16

  This paper examines formal methods for measuring semantic similarity in natural language processing. It discusses the concept of semantic similarity using mathematical and algorithmic models, such as vector-space…

• About the tasks of optimizing local network operation

  Alaminov, Muratbay Xaytbaevich, Аламинов, Муратбай Хайтбаевич, Alaminov, Muratbay Xaytbaevich · Ilim ha’m ja’miyet · 2026-05-16

  The article discusses the issues of optimizing the work of a local area network. Important methods for increasing the efficiency of local area network operations are discussed. It is shown what is important to pay…

• Determination of the refractive index of dispersed liquids according to snell’s law

  Akimova, Jumakhan Orazbaevna, Saburova, Surayyo Saparbaevna, Акимова, Джумахан Оразбаевна, Сабурова, Сурайё Сапарбаевна, Akimova, Jumaxan Orazbaevna, Saburova, Surayyo Saparbay qiz · Ilim ha’m ja’miyet · 2026-05-16

  This scientific paper examines a laboratory experiment to determine the refractive index of various dispersive liquids (water, toluene, etc.) using Snell's law with a hollow prism. The minimum deviation angle method was…

• Reconfiguration of interface charge states and its effect on the electro-physical properties of metal–dielectric–semiconductor structures

  Mamatkarimov, Odiljon Okhundedaevich, Abdulkhayev, Abrorbek Abdulloxonovich, Fazliddinov, Salokhiddin Bakhriddinovich, Quchqarov, Behzod Hoshimjonovich, Маматкаримов, Одилжон Охунд · Ilim ha’m ja’miyet · 2026-05-16

  This work analyzes the physical mechanisms responsible for non-ideal electrical effects in metal–dielectric–semiconductor (MDS) structures. The study is based on the kinetic properties of charge states located at the…

• Laser modification of basalt textile materials for functional applications in light industry

  Markevich, Maria Ivanovna, Asanov, Dauranbek Jadigerovich, Маркевич, Мария Ивановна, Асанов, Дауранбек Жадигерович, Markevich, Mariya Ivanovna, Asanov, Dauranbek Jadigerovich · Ilim ha’m ja’miyet · 2026-05-16

  The article The effect of laser radiation on basalt fabric TBK-100 was investigated in order to develop regimes for its controlled modification. The treatment was carried out at energy inputs of 60-240 J with a fixed…

• Engineering and economic bases of bitumen-distillate coating application

  Urinov, Abrorbek Axrorovich, Akhrorov, Amirkhon Abrorbekovich, Уринов, Аброрбек Ахрорович, Ахроров, Амирхон Аброрбекович, Urinov, Abrorbek Aksrorovich, Ahrorov, Amirxon Abrorbekovi · Ilim ha’m ja’miyet · 2026-05-16

  The article provides information on the relevance, economic efficiency and practical significance of the introduction of new anti-corrosion coatings. Bitumen-distillate compositions are cost-effective and…

• An intelligent system for detecting shoulder joint in radiographic images using deep learning

  Uteuliev, Nietbay Uteulievich, Djaykov, Gafur Muratbaevich, Artikbaev, Javlonbek Ziyatbaevichi, Sagidullaev, Nursultan Ibadullaevich, Утеулиев, Ниетбай Утеулиевич, Джайков, Гафур М · Ilim ha’m ja’miyet · 2026-05-16

  This paper presents a deep learning-based model for automatic shoulder fracture detection using EfficientNet-B0. The model was trained on the XR_SHOULDER subset of the MURA dataset. The achieved accuracy of about 80%…

• Influence of extended defects on the photoluminescent properties of znte/gaas epitaxial films

  Sharibaev, Murat Boribaevich, Yusupov, Oralbay Nauryzbaevich, Kalandarova, Shakhnoza Kuvondikovna, Шарибаев, Мурат Борибаевич, Юсупов, Оралбай Наурызбаевич, Каландарова, Шахноза Ку · Ilim ha’m ja’miyet · 2026-05-16

  In this work we report the depth inhomogeneity study of MBE grown ZnTe/(001) GaAs epilayers of different thickness by photoluminescence methods. The well profile change was calculated from PL peak energy shift. The role…

Ilim ha’m ja’miyet — barcha maqolalar · 2026-yil arxivi