Introduction of a New Variable Asa Universal Technique of the Solution of Rational Equations Above the Second Degree

The article reveals the role of equations at the basic and profi le levels of teaching students mathematics at school. Various ways of solving rational equations of the third and fourth degree, based on the technique of the introduction of a new variable, are demonstrated. This technique is universal in mathematics. It fi nds its application both in algebra, in the solution of inequalities, in equations and their systems, and in geometry, where the additionally constructed geometric fi gure — a segment, an angle, a circle, a triangle — appears as a new variable. The methods of solving rational equations, shown by the author in this article, will be especially useful and interesting for students of profi le classes, as well as for applicants and students of higher educational institutions and mathematics teachers.