求1/x(x+1)+2/(x+1)(x+3)+3/(x+3)(x+6)的值
问题描述:
求1/x(x+1)+2/(x+1)(x+3)+3/(x+3)(x+6)的值
答
1/x(x+1)+2/(x+1)(x+3)+3/(x+3)(x+6)
=1/x-1/(x+1)+1/(x+1)-1/(x+3)+1/(x+3)-1/(x+6)
= 1/x-1/(x+6)
=(x+6-x)/[x(x+6)]
=6/[x(x+6)]