1/((x-1)*(x-2))+1/((x-2)*(x-3))+1/((x-3)*(x-4)).+1/((x+2006)*(x-2007))很难,难于上青天!提示:是(x-1)*(x-2)分之一加上.,.是省略号,有关分式加减的

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 15:01:09
1/((x-1)*(x-2))+1/((x-2)*(x-3))+1/((x-3)*(x-4)).+1/((x+2006)*(x-2007))很难,难于上青天!提示:是(x-1)*(x-2)分之一加上.

1/((x-1)*(x-2))+1/((x-2)*(x-3))+1/((x-3)*(x-4)).+1/((x+2006)*(x-2007))很难,难于上青天!提示:是(x-1)*(x-2)分之一加上.,.是省略号,有关分式加减的
1/((x-1)*(x-2))+1/((x-2)*(x-3))+1/((x-3)*(x-4)).+1/((x+2006)*(x-2007))
很难,难于上青天!
提示:是(x-1)*(x-2)分之一加上.,.是省略号,有关分式加减的

1/((x-1)*(x-2))+1/((x-2)*(x-3))+1/((x-3)*(x-4)).+1/((x+2006)*(x-2007))很难,难于上青天!提示:是(x-1)*(x-2)分之一加上.,.是省略号,有关分式加减的
1/(x-1)(x-2)=1/(x-2)-1/(x-1)
同理
1/(x-2)(x-3)=1/(x-3)-1/(x-2)
1/(x-3)(x-4)=1/(x-4)-1/(x-3)
.
1/(x-2006)(x-2007)=1/(x-2007)-1/(x-2006)
1/((x-1)*(x-2))+1/((x-2)*(x-3))+1/((x-3)*(x-4)).+1/((x+2006)*(x-2007))
=1/(x-2)-1/(x-1)+1/(x-3)-1/(x-2)+1/(x-4)-1/(x-3)+...
+1/(x-2007)-1/(x-2006)
=1/(x-2007)-1/(x-1)
=(x+2006)/(x-1)(x-2007)