2/x^2+4x+3+2/x^2+8x+15+2/x^2+12x+35

问题描述:

2/x^2+4x+3+2/x^2+8x+15+2/x^2+12x+35

原式=2/(x+1)(x+3)+2/(x+3)(x+5)+2/(x+5)(x+7)
=1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+1/(x+5)-1/(x+7)
=1/(x+1)-1/(x+7)
=(x+7-x-1)/(x+1)(x+7)
=6/(x²+8x+7)