(Ax+B )(x+4) + C(x^2 +4)= x^2(A+B ) +x(B+4A)+4B+4C=3x-7 =>
A=1,B=-1,C=-3/4 =>

(3x-7)/(x^2 + 4)*(x+4) = (x-1)/(x^2 +4) - 3/4(x+4)