1/（X²+3X+2）+1/（X²+5X+6)+1/（X²+7X+12）=?

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/15 19:45:50
1/（X²+3X+2）+1/（X²+5X+6)+1/（X²+7X+12）=?
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1/（X²+3X+2）+1/（X²+5X+6)+1/（X²+7X+12）=?
1/（X²+3X+2）+1/（X²+5X+6)+1/（X²+7X+12）=?

1/（X²+3X+2）+1/（X²+5X+6)+1/（X²+7X+12）=?
1/（X²+3X+2）+1/（X²+5X+6)+1/（X²+7X+12）
=1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)
=1/(x+1)-1/(x+4)
=(x+4-x-1)/(x+1)(x+4)
=3/(x+1)(x+4)