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例1.当x取何值时,分式(x+1)/(x~2-1)有意义错解:原式=(x+1)/((x+1)(x-1))=1/(x-1)由分母x-1≠0得x=1∴当x≠1时,原分式有意义。分析:讨论分式有无意义时,要注意对原分式进行讨论,不能在约分后再讨论。因为在约分后常会使未知数取值范围扩大。因此上述解法是错误的。正确的解法是:当分母x~2-1≠0时,即x≠±1时,原分式才有
Example 1. The meaning of the fractional (x + 1) / (x ~ 2-1) is wrongly interpreted when the value of x is taken into consideration: The original = (x + 1) / (x + 1) ) = 1 / (x-1) x = 1 from denominator x-1 ≠ 0 The original fraction makes sense when x ≠ 1. Analysis: Discussion Fractional meaningless, pay attention to the original fractional discussion, can not be discussed after about points. Because after the points often unknowns to expand the range of values. So the above solution is wrong. The correct solution is: when the denominator x ~ 2-1 ≠ 0, that is, x ≠ ± 1, the original fraction