Evaluate the limit using the appropriate properties of limits$.$ lim$$x$$$(6$x$^27)/5$x$^2+$ x $3$

We are given the following.

lim$$x$$$$

$6$x$275$x$2+$ x $3$

We note that as x becomes large, both the numerator and the denominator become large. Therefore, it is not immediately obvious what happens to their ratio. So$,$ we need to do some preliminary algebra. Recall that to evaluate the limit of a rational function at infinity, we first divide both the numerator and the denominator by the highest power of x that occurs in the denominator.

Therefore, we should divide the numerator and the denominator by which of the following?

x

x$^2$

x$^3$

x$^4$