1/X²+3X+2 +1/X²+5X+6 +1/X²+7X+12 +1/X²+9X+20
问题描述：
1/X²+3X+2 +1/X²+5X+6 +1/X²+7X+12 +1/X²+9X+20
答
原式= 1/(x+1)(x+2) + 1/(x+2)(x+3) + 1/(x+3)(x+4) + 1/(x+4)(x+5)= (x+3+x+1) / [ (x+1)(x+2)(x+3) ] + (x+5+x+3) / [ (x+3)(x+4)(x+5)]= 2 / [(x+1)(x+3)] + 2/ [(x+3)(x+5)]= [2(x+5)+2(x+1)] / [ (x+1)(x+3)(x+...