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近日,笔者在研究中考试题时发现,2013年广东省珠海市中考数学试卷中第五题20小题第(2)问值得商榷,试分析如下:原题阅读下面材料,并解答问题.材料:将分式(-x~4-x~2+3)/-x~2+1拆分成一个整式与一个分式(分子为整数)的和的形式.解由于分母为-x~2+1,可设-x~4-x~2+3=(-x~2+1)(x~2+a)+b,则-x~4-x~2+3=(-x~2+1)(x~2+a)+b=-x~4-ax~2+x~2+a+b=-x~4-(a-1)x~2+(a+b)∵对于任意x,上述等式均成立,∴(?).
Recently, the author found in the study exam questions, 2013 Zhuhai City, Guangdong Province in the math test paper fifth question 20 small question (2) is questionable, test analysis is as follows: The original title to read the following materials and answer questions.Material: Divide the fraction (-x ~ 4-x ~ 2 + 3) / - x ~ 2 + 1 into a sum of an integral and a fraction (numerator). Since the denominator is -x ~ 2 + 1, -x ~ 4-x ~ 2 + 3 = (- x ~ 2 + 1) (x ~ 2 + a) + b +1) (x ~ 2 + a) + b = -x ~ 4-ax ~ 2 + x ~ 2 + a + b = -x ~ 4- (a-1) x ~ 2 + (a + b) For any x, the above equations hold, ∴ (?).