[1/(x+1)-(x+3)/(x^2-1)*(x^2-1)/(x^2+4x+3)]/[2/(x+1)]
=[1/(x+1)-(x+3)/[(x^2-1)](x^2-1)/[(x+3)(x+1)]]/[2/(x+1)]
=[1-(x^2-1)/(x-1)]/2
=1/2-(x+1)/2
=(1-√3)/2