[tex]\frac{x^{2} + x - 12}{4x^{2} - x - 3} = \frac{x^{2} + 4x - 3x - 12}{4x^{2} - 4x + 3x - 3} = \frac{x(x) + x(4) - 3(x) - 3(4)}{4x(x) - 4x(1) + 3(x) - 3(1)} = \frac{x(x + 4) - 3(x + 4)}{4x(x - 1) + 3(x - 1)} = \frac{(x - 3)(x + 4)}{(4x + 3)(x - 1)}[/tex]
