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换元法是数学的一种非常重要的思想方法,就是用新的未知数去代换题中含有原未知数表达式,达到化繁为简,化难为易,沟通已知和未知的联系,使复杂问题符合学生已有的知识系统,从而把认知过程内化成符合学生思维可认知过程.换元思想在中学数学极为广泛的应用,尤其是在求解分式方程中,能够把分式方程转化为整式方程,从而变得易求易解.换元要注意新旧变元的取值范围的变化.要避免代换的新变量的取值范围被缩小;若新变量的取值范围扩大了,则在求解之后要加以检验.本文通过例题详解说明四种常见换元法解分式方程的过程,以期找到运用这种方法解分式方程的一般策略.
The replacement method is a very important method of thinking in mathematics. It is to use new unknowns to replace original expressions with unknown expressions, to achieve simplicity, to make it difficult to understand, to communicate with known and unknown connections, and to make complex. The problem is in line with the student’s existing knowledge system, thereby transforming the cognitive process into a student-thinking cognitive process. The meta-analysis is widely used in middle school mathematics, especially in solving fractional equations, which can be transformed into fractional equations. For the whole equation, it becomes easy to solve. The new element should pay attention to the change of the range of the old and new variables. To avoid the replacement of new variables, the range of values is reduced; if the range of new variables is enlarged, After the solution, it should be tested. This article explains the process of solving the fractional equations by four common substitution methods through an example to find a general strategy for solving fractional equations using this method.