Evaluate the limit if it exists. If the limit does not exist, enter DNE.

$\underset{t-2}{lim}\frac{t2}{t^{3}8}=$

$$

Hint: Substituting $t=-2$ into the rational function yields $\frac{0}{0},$ so we cannot use direct substitution to evaluate the limit$.$ But we have the following useful fact. If $f(x)=g(x)$ except possibly at $x=a,$ then $\underset{xa}{lim}f(x)=\underset{xa}{lim}g(x).$ This means that we may be able to factor the sum or difference of two cubes and simplify before evaluating the limit$.$