论文部分内容阅读
分式方程的增根与无解是学习分式方程中常见的两个重要概念,两者既有区别,又有密切的联系,须慎重不能等同.当把分式方程转化为整式方程的变形过程中,使分母的值为零的这种限制被取消了,从而原方程中未知数的取值范围扩大了,导致转化后的整式方程的根恰好是原方程未知数的允许值范围之外的值,从而产生了不是原方程的根,即分式方程的增根;而分式方程无解有两种情况,其一是变形后的整式方程本身无解,其二是整式方程有解,但这些解使最简公分母的值都为零,即为分式方程的增根.
The root and non-solution of fractional equation are two important concepts that are common in learning fractional equation. The two are not only the same but also the close relation, which can not be equated.When the fractional equation is transformed into the deformation of integral equation In the process, the restriction that the value of denominator is zero is canceled, so that the range of the unknowns in the original equation is expanded so that the root of the converted integral equation is just outside the allowable value range of the original equation unknowns , Resulting in the root of the original equation that is not the original equation, that is, the root of fractional equation; and fractional equation no solution, there are two cases, one is the deformed integral equation itself has no solution, the other is the integral equation has solution, but the solution These solutions make the value of the simplest denominator zero, which is the root of the fractional equation.