The some theoretical aspects of teaching students to solve the rational equations, which are reduced to square equations

The content line of equations and inequalities is one of the main in the school algebra’s curricula. It has a branched system of intrinsic and intersubject connections. The mastering of different methods of solving various types of equations their systems including square ones, and those reduced to such, and their systems contributes to the development of students’ thinking, memory, intuition, the ability to find a way out of non-standard situations. This mastering also plays a propaedeutic role in studying other chapters of natural sciences and mathematics.

The variable substitutions’ method a traditionally causes some difficulties for students. Therefore, there are considered some types of rational equations, which are reduced to square equations by using the corresponding transformations and variables substitutions in the article. All types of reviewed equations are studied in the course of algebra of the 8th year, in-depth level of education. They are 1) , where ; 2) , where ; ;  where ;  are some functions; ; . There are provided methodological comments on solution and relevant examples for each type of reviewed equations.