$ 10A = \dfrac{10^{16} +10}{10^{16}+1} = \dfrac{(10^{16} +1)+9}{10^{16}+1}$
$ = \dfrac{10^{16} +1}{10^{16}+1} + \dfrac{9}{10^{16}+1} = 1 + \dfrac{9}{10^{16}+1}$
$ 10B = \dfrac{10^{17} +10}{10^{17}+1} = \dfrac{(10^{17} +1)+9}{10^{17}+1}$
$ = \dfrac{10^{17} +1}{10^{17}+1} + \dfrac{9}{10^{17}+1} = 1 + \dfrac{9}{10^{17}+1}$
Ta có $ 10^{16}+1 < 10^{17}+1 \to \dfrac{9}{10^{16}+1} > \dfrac{9}{10^{17}+1}$
$\to 1 + \dfrac{9}{10^{16}+1} > \dfrac{9}{10^{17}+1}$
$\to 10A > 10B$
$\to A > B$
