I know that infinity plugged into any (where n is a variable to any power) is zero.
There is no such thing as "plugging in infinity" as infinity is not a number. However, you notice that the behaviour of a fraction with an increasing denominator is to get smaller.
Anyway, start by dividing the top and bottom of both fractions by the highest power of x.
the limit of that equation is 3.
Like prove it said, you should divide by the biggest degree which in this case is 6. when you divide the denominator by 6, be sure to first multiply the 6 * 1/2 as the degree is being taken out of the squareroot.