Ta có :
\(A=\frac{10^{15}+1}{10^{16}+1}=\frac{\left(10^{15}+1\right).10}{\left(10^{16}+1\right).10}=\frac{10^{16}+10}{10^{17}+10}\)
\(\Rightarrow A=\frac{10^{16}+1+9}{10^{17}+1+9}\)
Vì \(\frac{10^{16}+1}{10^{17}+1}< \frac{10^{16}+1+9}{10^{17}+1+9}\)
Mà \(A=\frac{10^{16}+1+9}{10^{17}+1+9}\)nên \(A>B\)
Vậy \(A>B\)