(3/(x+4) + 6x/(x^2 + x - 12) - 1/(x-3)) : (8x - 13)/(x^2 - 16) =
(3/(x+4) - 1/(x-3) + 6x/(x^2 + x - 12)) * (x^2 - 16)/(8x - 13) =
((3x - 9 -x - 4)/(x-3)(x+4) + 6x/(x^2 + x - 12)) * (x^2 - 16)/(8x - 13) =
((2x -13)/(x^2 + x - 12) + 6x/(x^2 + x - 12)) * (x^2 - 16)/(8x - 13) =
((8x -13)/(x^2 + x - 12)) * (x^2 - 16)/(8x - 13) =
(x^2 - 16)/(x^2 + x - 12) = (x-4)(x+4)/(x-3)(x+4) = (x - 4)/(x-3) = 1-1/(x-3)