化简(x-1)(x-2)分之一+(x-2)(x-3)分之一+……(x-n)(x-n-1)分之一

1.
1/(x-1)(x-2)+1/(x-2)(x-3).+1/(x-n)(x-n-1)
=[1/(x-2)-1/(x-1)]+[1/(x-3)-1/(x-2)]+.+[1/(x-n-1)-1/(x-n)]
=1/(x-n-1)-1/(x-1)
=n/(x-1)(x-n-1)
2.
m-n=a+2/a+3-a+1/a+2=1/(a+3)(a+2),因为a＜-3,所以a+3＜0,a+2＜-1,所以(a+3)(a+2)＞0,所以1/(a+3)(a+2)＞0,所以m-n＞0,所以M＞N；
同理：N＞P,
所以：M＞N＞P

(x-1)(x-2)分之一+(x-2)(x-3)分之一+……(x-n)(x-n-1)
=-（1/（x-1)-1/(x-2)+1/(x-2)-1/（x-3)+……1/（x-n)-1/(x-n-1))
=-(1/(x-1)-1/(x-n-1))
=1/(x-n-1)-1/(x-1)
令a=-4
则m=2，n=3/2，p=4/3
所以p＜m＜n
选D
祝你开心！

(x-1)(x-2)分之一+(x-2)(x-3)分之一+……(x-n)(x-n-1)分之一=(x-n-1)分之一-(x-1)分之一
m-n=1-a/6>0
n-p=1-a/2>0
选c