What is the equation of the horizontal asymptote of f(x) = (3x+6)/(x-5)?

For a rational function whose numerator and denominator have the same degree, the horizontal asymptote is the ratio of the leading coefficients. Here the leading coefficients are 3 and 1, so $y = \frac{3}{1} = 3$, choice A. Intuitively, when $x$ is huge, the constants $+6$ and $-5$ are negligible, and $\frac{3x}{x} = 3$. Choice B ($y = 5$) is wrong because 5 gives the vertical asymptote, where the denominator is zero. Choice C ($y = 6$) uses the constant of the numerator. Choice D ($x = 5$) is that vertical asymptote, which is a vertical line and not a horizontal asymptote.