Assuming the limit is taken as n approaches infinity, we have
[tex]\displaystyle\lim_{n\to\infty}\frac{6n^2-2n}{n^2+8}=\lim_{n\to\infty}\frac{6-\frac2n}{1+\frac8{n^2}}=\boxed6[/tex]
because the rational terms in the numerator and denominator will vanish.
