Evaluate the following limit without L'Hopital I tried to evaluate the following limits but I just couldn't succeed, basically I can't use L'Hopital to solve this... 
for the second limit I tried to transform it into  $e^{\frac{2n\sqrt{n+3}ln(\frac{3n-1}{2n+3})}{(n+4)\sqrt{n+1}}}$ but still with no success...
$$\lim_{n \to \infty } \frac{2n^2-3}{-n^2+7}\frac{3^n-2^{n-1}}{3^{n+2}+2^n}$$
$$\lim_{n \to \infty } \frac{3n-1}{2n+3}^{\frac{2n\sqrt{n+3}}{(n+4)\sqrt{n+1}}}$$
Any suggestions/help? :)
Thanks

Hints :
$$ \frac{2n^2-3}{-n^2+7}  = \frac{2 - \frac{3}{n^2}}{-1+\frac{7}{n^2}},$$
and
$$ \frac{3^n-2^{n-1}}{3^{n+2}+2^n} = \frac{1-\frac{1}{2}\left( \frac{2}{3} \right)^n}{3^2+\left( \frac{2}{3} \right)^n}.$$
