$A = \dfrac{15^{16}+1}{15^{17}+1} $
$⇒15A = \dfrac{15^{17}+15}{15^{17}+1} = 1+\dfrac{14}{15^{17}+1} $
$B =\dfrac{15^{15}+1}{15^{16}+1} $
$ ⇒15A = \dfrac{15^{16}+15}{15^{16}+1} = 1+\dfrac{14}{15^{16}+1} $
Vì $15^{17}+1 > 15^{16}+1$
$⇒ \dfrac{14}{15^{17}+1} < \dfrac{14}{15^{16}+1} $
$⇒1+ \dfrac{14}{15^{17}+1} < 1+\dfrac{14}{15^{16}+1} $
$⇔15A < 15B$
$⇔A<B$