题目

(明天就开学了)
解方程:1.x+1/x+2 + x+6/x+7=x+5/x+6 + x+2/x+3(最好有过程)
2.1/x-1 + 1/x-7=1/x-2 + 1/x-6
3.1/(x+1)(x+2) + 1/(x+2)(x+3) + .+1/(x+2007)(x+2008)=x+2006/2x+4016

提问时间：2021-10-14

答案

1
x+1/x+2-x+2/x+3=x+5/x+6-x+6/x+7
((X^2+4X+3)-(X^2+4X+4))/(X^2+5X+6)=((X^2+12X+35)-(X^2+4X+36)/(X^2+13X+42)
-1/(X^2+5X+6)=-1/(X^2+13X+42)
X^2+5X+6=X^2+13X+42
X=-4.5
2
过程类似于1
X=4
3
1/(x+1)(x+2) + 1/(x+2)(x+3) + .+1/(x+2007)(x+2008)
＝1/(x+1)-1/（X+2)+1/(X+2)-1/(X+3)+.+1/(X+2007)-1/(X+2008)
=1/(x+1)-1/(X+2008)
1/(x+1)-1/(X+2008)=x+2006/2x+4016
1/(x+1)=x+2006/2x+4016+1/(X+2008)=x+2006/2x+4016+2/(2X+4016)=x+2008/2x+4016=0.5
X=1