原式=1/x(x-1)+1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
=1/(x-1)-1/x+1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)
=1/(x-1)-1/(x+3)
=4/(x²+2x-3)