Question

Evaluate: The limit as x goes to infinity of (3-7x^4)/(5+3x^4)

Answer 1

apply l'hospitals

Answer 2

or just notice that we can take the ratio of the coefficients

Answer 3

i like second method better, especially since you probably did not learn l'hopital's rule yet.
the degree of the numerator is equal the degree of the denominator, so take the ratio of the leading coefficients as langrange said