Explanation:
limit for n going to what ?
I think you mean n going to ±infinity.
for very large n (when n goes to infinity) such a fraction is reduced to the ratio of the terms with the highest exponents of n. the terms with lower exponents simply get less and less impact with growing n, and fade away for really, really large n going to infinity.
so, this limit evaluation is reduced to
lim n²/(3n³ + n²) = 1/(3n + 1)
which is again for very large n
lim 1/(3n), which goes to 1/infinity = 0
the same for going to 1/-infinity = 0
if you meant e.g. limit for n going to 0, then for the limit we set n to 0 and see, that all terms are turning 0, except for the constants -5 in the numerator and +7 in the denominator.
so, that limit is then
-5/7 = -0.714285714...