`Answer:`
Ảnh mờ quá nên mình có làm sai đề thì bạn bảo nhé.
\(A=\frac{10^{2011}+1}{20^{2012}+1}\)
\(\Rightarrow10A=\frac{10^{2012}+10}{10^{2012}+1}=1+\frac{9}{10^{2012}+1}\)
\(B=\frac{10^{2012}+1}{10^{2013}+1}\)
\(\Rightarrow10B=\frac{10^{2013}+10}{10^{2013}+1}=1+\frac{9}{10^{2013}+1}\)
Mà \(10^{2012}+1< 10^{2013}+1\)
\(\Rightarrow\frac{9}{10^{2012}+1}>\frac{9}{10^{2013}+1}\)
\(\Rightarrow1+\frac{9}{10^{2012}+1}>1+\frac{9}{10^{2013}+1}\) hay \(10A>10B\)
Vậy `A>B`
B<102012+1+9102013+1+9=102012+10102013+10=10(102011+1)10(102012+1)=102011+1102012+1=A
Vậy A > B
