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!

Yes we can divide by $X^3$ but we obtain
$$\frac{5X^2 + 8X - 3}{3X^2 + 2}=\frac{\frac 5 X + \frac 8{X^2} - \frac 3{X^3}}{\frac 3X + \frac2{X^3}}$$
which is again an indeterminate form.
In general, to avoid that this happens, the standard way is to factor out the dominating term from the numearator and the denominator.
