For others who might be interested, the simples thing to do is divide both numerator and denominator by "x":
[tex]\lim_{x\to\infty} \frac{3x+ 5}{x- 4}= \frac{3+ \frac{5}{x}}{1- \frac{4}{x}}[/tex]
Now, as x goes to infinity, the terms with x in the denominator go to 0.