解方程:(1/x²+3x+2)+(1/x²+5x+6)+(1/x²+7x+12)+(1/x
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/26 07:29:43
解方程:(1/x²+3x+2)+(1/x²+5x+6)+(1/x²+7x+12)+(1/x²+9x+20)=1/8
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)(x+5)=1/8
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)=1/8
1/(x+1)-1/(x+5)=1/8
(x+5-x-1)/(x+1)(x+5)=1/8
32=x²+6x+5
x²+6x-27=0
(x+9)(x-3)=0
x=-9 x=3
检验:x=-9 x=3是方程的解
再问: 为什么是这么写呢?1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)=1/8
再答: 裂项 看一个 1/(x+1)(x+2)=[(x+2)-(x+1)]/ (x+1)(x+2) =(x+2)/(x+1)(x+2)-(x+1)/(x+1)(x+2) =1/(x+1)-1/(x+2)
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)=1/8
1/(x+1)-1/(x+5)=1/8
(x+5-x-1)/(x+1)(x+5)=1/8
32=x²+6x+5
x²+6x-27=0
(x+9)(x-3)=0
x=-9 x=3
检验:x=-9 x=3是方程的解
再问: 为什么是这么写呢?1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)=1/8
再答: 裂项 看一个 1/(x+1)(x+2)=[(x+2)-(x+1)]/ (x+1)(x+2) =(x+2)/(x+1)(x+2)-(x+1)/(x+1)(x+2) =1/(x+1)-1/(x+2)
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