(6x - 5) / (x^2 - 4x - 21) - (7x + 9) / (x^2 - x - 12) + (x - 6) / (x^2 -11x + 28)
= (6x - 5) / (x - 7)(x + 3) - (7x + 9) / (x - 4)(x + 3) + (x - 6) / (x - 7)(x - 4)
= (6x - 5)(x - 4) / (x - 7)(x + 3)( x - 4) - (7x + 9)(x - 7) / (x - 7)(x + 3)(x - 4) + (x - 6)(x + 3) / (x - 7)(x + 3)(x - 4)
= (6x^2 - 29x + 20) / (x - 7)(x + 3)(x - 4) - (7x^2 - 40x - 63) / (x - 7)(x + 3)(x - 4) + (x^2 - 3x - 18) / (x - 7)(x + 3)(x - 4)
= ((6x^2 - 29x + 20) - (7x^2 - 40x - 63) + (x^2 - 3x - 18)) / (x - 7)(x + 3)(x - 4)
= (6x^2 - 29x + 20 - 7x^2 + 40x + 63 + x^2 - 3x - 18) / (x - 7)(x + 3)(x - 4)
= (8x + 65) / (x - 7)(x + 3)(x - 4)
This cannot be simplified any futher.