Limit to infinity rule for fractions? I am reading a book and it says to solve limits to infinity with a fraction such as:
$$\frac{5X^2 + 8X - 3}{3X^2 + 2}$$
We divide the numerator and denominator by the highest power of X in the DENOMINATOR so in this case it is $X^2$.  I get this helps simplify the equation, but what is to prevent someone from dividing by a higher power like $X^3$?  All components would evaluate to 0.
Is there another rule for limits that I am not aware of?
Thanks!

The most dominant term in num is $5x^2$ and the most dominant term in den is $3x^2$
when $x$ is very large. So the required limit is $$L=\lim_{x\to \infty} \frac{5x^2}{3x^2}=\frac{5}{3}.$$
