(1)
1/[n*(n+1)]=1/n-1/(n+1)
证明：
1/n-1/(n+1)
=(n+1)/[n*(n+1)]-n/[n*(n+1)]
=1/[n*(n+1)]
1/(x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2).
=[1/(x-3)-1/(x-2)]-[1/(x-3)-1/(x-1)]+[1/(x-2)-1/(x-1)]
=1/(x-3)-1/(x-2)-1/(x-3)+1/(x-1)+1/(x-2)-1/(x-1)
=0
(2)
(x^2-1)/(x-2)(x-3)=a+b/(x-2)+c/(x-3)
(x+1)(x-1)/(x-2)(x-3)=a+b/(x-2)+c/(x-3)
[(x+1)/(x-2)]*[(x-1)/(x-3)]=a+b/(x-2)+c/(x-3)
[1+3/(x-2)]*[1+2/(x-3)]=a+b/(x-2)+c/(x-3)
1+3/(x-2)+2/(x-3)+6/(x-2)(x-3)=a+b/(x-2)+c/(x-3)
1+3/(x-2)+2/(x-3)+6/(x-3)-6/(x-2)=a+b/(x-2)+c/(x-3)
1-3/(x-2)+8/(x-3)=a+b/(x-2)+c/(x-3)
a=1,b=-3,c=8