Đặt \(A=\frac{10^{15}+1}{10^{16}+1}\Rightarrow10A=\frac{10^{16}+10}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)
Đặt \(B=\frac{10^{16}+1}{10^{17}+1}\Rightarrow10B=\frac{10^{17}+10}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)
Vì \(10^{16}+1< 10^{17}+1\Rightarrow\frac{9}{10^{16}+1}>\frac{9}{10^{17}+1}\)
\(\Rightarrow10A>10B\Rightarrow A>B\)
\(\Rightarrow\frac{10^{15}+1}{10^{16}+1}>\frac{10^{16}+1}{10^{17}+1}\)