1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)+1/(x^2+9x+20)
=1/﹙x+1﹚﹙x+2﹚+1/﹙x+2﹚﹙x+3﹚+1/﹙x+3﹚﹙x+4﹚+1/﹙x+4﹚﹙x+5﹚
=1/﹙x+1﹚-1/﹙x+2﹚+1/﹙x+2﹚-1/﹙x+3﹚+1/﹙x+3﹚-1/﹙x+4﹚+1/﹙x+4﹚-1/﹙x+5﹚
=1/﹙x+1﹚-1/﹙x+5﹚
=4/﹙x²+6x+5﹚
1/(x^2+3x+2)+1/(x^2+5x+6)+1/(x^2+7x+12)+1/(x^2+9x+20)
=1/﹙x+1﹚﹙x+2﹚+1/﹙x+2﹚﹙x+3﹚+1/﹙x+3﹚﹙x+4﹚+1/﹙x+4﹚﹙x+5﹚
=1/﹙x+1﹚-1/﹙x+2﹚+1/﹙x+2﹚-1/﹙x+3﹚+1/﹙x+3﹚-1/﹙x+4﹚+1/﹙x+4﹚-1/﹙x+5﹚
=1/﹙x+1﹚-1/﹙x+5﹚
=4/﹙x²+6x+5﹚