[tex] \frac{x^{3}+3x^{2}-4x-12}{x^{2}+5x+6} [/tex]
Factor bottom half:
[tex] \frac{x^{3}+3x^{2}-4x-12}{(x+3)(x+2)}[/tex]
Factor top half:
[tex]\frac{(x+3)(x^{2}-4)}{(x+3)(x+2)}[/tex]
Factor top (x^(2)-4) completely:
[tex]\frac{(x+3)(x-2)(x+2)}{(x+3)(x+2)}[/tex]
Cancel common terms:
[tex]\frac{(x+3)(x-2)(x+2)}{(x+3)(x+2)} = \frac{(x+3)(x-2)}{(x+3)} = (x-2)[/tex]
Your quotient is x-2.
