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在分式方程教学中,发现很多学生在解分式方程时,常常将增根和无解混为一谈,产生这种现象的原因是,没有真正去理解分式方程产生增根的原因.关于分式方程产生增根的原因,大多教师在教学时是这样解释的:解分式方程时,在把分式方程转化为整式方程的变形过程中,方程的两边都乘了一个可能使分母为零的整式,从而扩大了未知数的取值范围,而产生的未知数的值即为分式方程的增根.这样的解释往往使学生陷入概念困境,似懂非懂.
In the teaching of fractional equation, it is found that many students solve the fractional equation, the root of the solution is often mixed with no solution, the reason for this phenomenon is that there is no real reason to understand the fractional equation to produce root causes. Most of the teachers in teaching are explained as follows: In the solution of the fractional equation, in the process of transforming the fractional equation into the integral equation, both sides of the equation are multiplied by a factor that makes the denominator zero Integer, thus expanding the range of unknowns, and the resulting value of the unknown is the root of the fractional equation. Such explanations often make students into conceptual difficulties, understandable.