I'm going to assume the equation you are trying to solve is:
(3/(x+3)) - ((12x+19)/(x2+7x+12)) - ((5/(x+4)) =0
Notice that the quadratic factors into (x+4)(x+3) now using this as a common denominator gives"
3(x+4)-(12x+19)-5(x+3)/((x+4)(x+3)) = 0 expanding the numerator and collecting like terms gives
14x+22 = 0
so x=-22/14 or -11/7 and this satisfies the original equation