如何正确求解分式方程的增根和无解

How to Correctly Solve the Root Increase and No Solution of the Fractional Equation

学生对分式方程的增根与无解概念混淆,认为分式方程无解和分式方程有增根是同一回事,认为分式方程无解和分式方程有增根是同一回事,事实上并非如此。解分式方程一般都要去分母化为整式方程,而整式方程只有:有解与无解二种情况。当整式方程无解时,那么原来的分式方程也一定无解。当整式方程有解时,原来的分式方程就不一定也有解,因为分式方程有产生增根的可能,若整式方程的解代入原分式方程的所有分母中,只要有一个分母为零,这个整式方程的解就不是原分式方程的根,它是一个增根。

Students are confused with the concept of rooting and non-solution of fractional equations. It is considered that the fractional equation has no solution and the fractional equation has the same rooting. It is considered that the fractional equation has no solution and the fractional equation has the same rooting. This is not the case. The solution equations are generally denormalized to the integral equation, while the integer equations have only two cases: solution and no solution. When the equation of the whole equation has no solution, then the original fractional equation must have no solution. When the equation of the whole equation has a solution, the original fractional equation does not necessarily have a solution, because the fractional equation has the possibility of generating roots. If the solution of the integral equation is substituted into all the denominators of the original fractional equation, as long as one denominator has zero The solution to this equation is not the root of the original fractional equation, it is an extension.