解方程1\x^2+3x+2+1\x^2+5x+6+1\x^2+7x+12+1\x+4=3\2

1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+1/(x+4)=3/2
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)=3/2
1/(x+1)=3/2
x+1=2/3
x=-1/3