Answer:
The domain is (-∞, -3), (-3, 2), (2, ∞)
Step-by-step explanation:
Start by factoring the denominator. That 2x^2 + 2x - 12 is the same as 2(x^2 + x - 6), which also factors easily: 2(x + 3)(x - 2).
Setting this equal to 0 and solving for x gives us the equations of the two vertical asymptotes: {-3, 2}. These two values also define the domain; x cannot equal either -3 or 2, as that would lead to division by zero.
The domain is (-∞, -3), (-3, 2), (2, ∞)
