lim(x-->infinity) (3x + 5) / (x - 4)
I first worked it out by taking the limit of each number, and found the denominator to have a limit of 0. Would that make the limit of the whole equation = infinity?
Try multiplying the numerator and denominator by $\displaystyle \frac{1}{x}$
$\displaystyle \lim_{x \to \infty}\frac{3+\frac{5}{x}}{1-\frac{4}{x}}$
Now the limit is easy to compute becuase the terms $\displaystyle \frac{5}{x},\frac{4}{x}$ both go to zero leaving us with the limit equal to 3.