化简1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3),其中x^2+3x+1=0

题目

化简1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3),其中x^2+3x+1=0

答案

原式=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]
=1/x-1/(x+3)
=2/(x^2+3x)
=2/(-1)
=-2