解分式方程产生增根的主要原因是方程两边同乘以各分母的最简公分母,从而在转化为整式方程的过程中,未知数的取值范围扩大了.因此,解分式方程过程中产生的增根,虽不是原方程的根,但一定是所得整式方程的根.我们可据此讨论含参数的分式方程根的问题. 例1 若关于x的方程3/x+ax/x+1=2+3/x+1有增根,求a的值. 简解:原方程去分母,得3(x+1)+ax2=2x(x+1)+3x ①若原方程有增根,则这个增根应当使原方程中分式的分母为零,并 The main reason for the rooting of the solution fractural equation is that the two sides of the equation are multiplied by the simplest common denominator of each denominator. Therefore, in the process of conversion to the integral equation, the range of the unknown value is enlarged. Therefore, the solution to the fractional equation is in the process. The resulting root addition, although not the root of the original equation, must be the root of the resulting integral equation. We can discuss the problem of the fractional equation root with parameters accordingly. Example 1 Equation 3/x+ax/x for x +1=2+3/x+1 increase root, find the value of a. Simple Explanation: The original equation to the denominator, get 3 (x +1) + ax2 = 2x (x +1) + 3x 1 if the original equation has increased Root, then this rooting should make the denominator of the fraction in the original equation zero, and