一道今天要答案的数学题1/(x+1)-1/(x+2)-1(x+3)+1/(x+4)
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一道今天要答案的数学题1/(x+1)-1/(x+2)-1(x+3)+1/(x+4)
一道今天要答案的数学题
1/(x+1)-1/(x+2)-1(x+3)+1/(x+4)
一道今天要答案的数学题1/(x+1)-1/(x+2)-1(x+3)+1/(x+4)
把整个式子同时乘于(x+1)(x+2)(x+3)(x+4)
同时除于(x+1)(x+2)(x+3)(x+4)
仔细观察分子上的算式,其实很简单的,大概写一下:分母为(x+1)(x+2)(x+3)(x+4)
分子为(x+2)(x+3)(x+4)-(x+1)(x+3)(x+4)-(x+1)(x+2)(x+4)+(x+1)(x+2)(x+3)
两两合并:比如前面两式把同样的(x+3)(x+4)可以提出来剩下(x+2)和(x+1)相减正好等于1 所以前面两式结果即为:(x+3)(x+4)=x^2+7x+12
同理由得后面两式结果为:-(x^2+3x+2) 合并一下 分子为4x+10
综:原式=4x+10/[(x+1)(x+2)(x+3)(x+4)]
1/(x+1)-1/(x+2)-1(x+3)+1/(x+4)
=[1/(x+1)+1/(x+4)]-[1/(x+2)+1(x+3)]
=(2x+5)[1/(x+1)(x+4)-1/(x+2)(x+3)]
=(2x+5)(6-4)/[(x+1)(x+4)(x+2)(x+3)]
=(4x+10)/[(x+1)(x+4)(x+2)(x+3)]