x^2+4x+2/x^2+4x+3-x^2+7x+5/x^2+7x+6

x^2+4x+2/x^2+4x+3-x^2+7x+5/x^2+7x+6

(x²+4x+2)/(x²+4x+3)-(x²+7x+5)/(x²+7x+6)
=(x²+4x+2)/(x+1)(x+3)-(x²+7x+5)/(x+1)(x+6)
=[(x+6)(x²+4x+2)-(x+3)(x²+7x+5)]/(x+1)(x+3)(x+6)
=[x³+4x²+2x+6x²+24x+12-(x³+7x²+5x+3x²+21x+15)]/(x+1)(x+3)(x+6)
=-3/(x+1)(x+3)(x+6)