Final answer:
The equation of the horizontal asymptote of the function f(x)= 2/(x+2) − (x+3)/(x+4) is y = 0.
Step-by-step explanation:
The equation of the horizontal asymptote can be found by analyzing the behavior of the function as x approaches positive or negative infinity. In this case, the given function is f(x) = 2/(x+2) - (x+3)/(x+4). Let's simplify it to get a better understanding of its behavior:
f(x) = (2(x+4) - (x+3)(x+2))/(x+2)(x+4)
Simplifying further, we get:
f(x) = (2x + 8 - x² - 7x - 6)/(x² + 6x + 8)
As x approaches positive or negative infinity, the highest degree term dominates the function. In this case, the highest degree term is x². Therefore, the horizontal asymptote of the function is y = 0.