分式方程的增根的利用

• 作 者: 罗家友
• 机 构: 保显农场中学
• 出 处: 数学学习
• 发表日期: 2004年03期
• 关键词: 增根 一元二次方程 整式方程 最简公分母 实数根 课外书籍 方程化

解分式方程的基本思想是 :把分式方程“转化”为整式方程 ,然后解整式方程 ,再进行验根 .如果求得的整式方程的根使分式方程的分母或最简公分母为 0 ,这些根叫增根 .分式方程的增根实质上是由分式方程化成的整式方程的根 ,使整式方程成立 ,却使分式方程无意义或不成立 .近年来

The basic idea of ​​solving fractional equations is: “convert” fractional equations into integral equations, then solve integral equations, and perform root verification. If the root of the resulting integral equation is such that the denominator or the most common common denominator of the fractional equation is 0, these roots are called roots. The rooting of the fractional equation is essentially the root of the integral equation formed by the fractional equation, which makes the integral equation true, but makes the fractional equation meaningless or inconclusive.