Final answer:
The equation of the oblique asymptote for h(x) = (x² - 3x - 4) / (x + 2) is y = x - 5, after performing long division of the numerator by the denominator.
Step-by-step explanation:
The equation of the oblique asymptote for the function h(x) = (x² - 3x - 4) / (x + 2) can be found by long division or synthetic division, as this function is a rational function where the degree of the numerator is exactly one higher than the denominator. In such cases, the oblique asymptote is the quotient of the division without the remainder.
To find the oblique asymptote, divide x² - 3x - 4 by x + 2. The division gives us x - 5 with a remainder, which we can disregard when it comes to finding the asymptote.
Therefore, the equation of the oblique asymptote is y = x - 5, which corresponds to option b from the given choices.