[Suwiwat B]

$\frac{2^{n+1}-2^{n-1}}{2^{n+2}-2^{n-2}}$
$= \frac{2^{n-1}(2^2 - 1)}{2^{n-2}(2^4-1)}$
$= 2^{(n-1) - (n-2)}\frac{4-1}{16-1}$
$= 2(\frac{3}{15})$
$= \frac{2}{5}$