作业帮1/(x+1)(x+2) + 1/(x+2)(x+3) + 1/(x+3)(x+4) + 1/(x+4)(x+5)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/15 16:19:41
1/(x+1)(x+2) + 1/(x+2)(x+3) + 1/(x+3)(x+4) + 1/(x+4)(x+5)
1/(x+1)(x+2) + 1/(x+2)(x+3) + 1/(x+3)(x+4) + 1/(x+4)(x+5)
1/(x+1)(x+2) + 1/(x+2)(x+3) + 1/(x+3)(x+4) + 1/(x+4)(x+5)
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)
=1/(x+1)-1/(x+5)
=-6/(x^2+6x+5)
我从别处COPY的 希望对你有用
利用1/n(n+1)可分解成为1/n-1/(n+1)，
例式可变为：
1/(x+1)-1/(x+2) + 1/(x+2)-1/x+3) + 1/(x+3)-1/(x+4) + 1/(x+4)-1/(x+5)
这下不用说了吧？
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分解因式----（X*X-X)(X*X-X-2)+1
】x(x+1)+x^2(x-1)
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