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解分式方程时,为了化分式方程为整式方程,需要用分式方程中各分式的最简公分母去乘分式方程的两边,如果所得的解恰好使最简公分母为0,那么这个解就是这个分式方程的增根.由此,分式方程的增根必满足两个条件:(1)增根一定是分式方程转化所得的整式方程的解;(2)增根使分式方程的分母为0.利用增根的这一特性可解决许多问题.
To solve the fractional equation, in order to convert the fractional equation to the integral equation, the simplest common denominator of each fraction in the fractional equation must be used to multiply the two sides of the fractional equation. If the resulting solution happens to make the simplest common denominator zero, Then the solution is the rooting of this fractional equation. Thus, the rooting of the fractional equation must satisfy two conditions: (1) The rooting must be the solution of the integral equation obtained by the conversion of the fractional equation; The denominator of the fractional equation is 0. Using this feature of increasing root can solve many problems.