论文部分内容阅读
分式方程,是一种重要的基本方程形式,也是初中数学的一个极大难点,尤其是在求解中,为了防止误将增根当成其根,常需要验根,基本解题步骤为:化分式方程为整式方程→确定整式方程的根→验根得到分式方程的根.求解思路明晰、过程明了,但仍有不少同学忘记验根,或者验根方法不科学,从而发生失误.本文提出了一种不需要验根的求解办法,供同学们参考.例1解方程1/x-2+3=1-x/2-x.分析1/x-2+3=1-x/2-x具有两方面的意义,①其整式方程1+3(x-2)=-(1-x)成立;②分式1/x-2、1-x/2-x都有意义,由分母不能为零,可知x-2≠0.据此,可以从分式方程的本质上,得到它的真正等价形式,具体解答如下:
Fractional equation, is an important form of basic equations, but also a mammoth junior high school mathematics, especially in the solution, in order to prevent mistakenly rooted as the root, often need to test the root, the basic steps to solve the problem: Fractional equation → integer equation → determine the root of the integral equation → root-test to get the root of the fractional equation. The solution is clear, the process is clear, but there are still many students forget to test the root, or root-test method unscientific, resulting in errors. In this paper, we propose a solution that does not require a root-mean-square test. For example, solve Equation 1 / x-2 + 3 = 1-x / 2-x. Analyze 1 / x-2 + 3 = 1-x / 2-x has two meanings: ① its integral equation 1 + 3 (x-2) = - (1-x) holds true; ② fractional 1 / x-2,1-x / 2-x has meaning , From the denominator can not be zero, we can see that x-2 ≠ 0. Accordingly, from the essence of fractional equation, its true equivalent form, the specific answer is as follows: