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学生在学习分式方程时,往往会忽略方程有增根与方程无解的具体差别。虽然这是一个细节性的问题,但却常常是解决很多分式方程问题的关键所在。其实方程是否有解与方程是否有增根是有着本质的区别,它们之间是不能划等号的。就分式方程增根与无解的区别与联系问题,首先从概念入手阐明增根与无解的关系,再通过实例进行认知强化。
When students learn fractional equations, they often neglect the specific differences between the incremental roots and the equations without solutions. While this is a matter of detail, it is often the crux of the solution to many fractional equation problems. In fact, there is an essential difference between whether the equation has solutions and whether there is an increase in the equation, and they can not be equated with each other. On the difference and connection between the root of a fractional equation and no solution, this paper first clarifies the relationship between the root of the solution and no solution from the concept, and then strengthens the cognition through examples.