Ta có:
\(A=\frac{20^{10}+1}{20^{10}-1}\)
\(=\frac{20^{10}-1+2}{20^{10}-1}\)
\(=1+\frac{2}{20^{10}-1}\)
\(B=\frac{20^{10}-1}{20^{10}-3}\)
\(=\frac{20^{10}-3+2}{20^{10}-3}\)
\(=1+\frac{2}{20^{10}-3}\)
Ta lại có:
\(20^{10}-1>20^{10}-3\)
\(\Rightarrow\)\(\frac{2}{2^{10}-1}< \frac{2}{2^{10}-3}\)
\(\Rightarrow\)\(1+\frac{2}{2^{10}-1}< 1+\frac{2}{2^{10}-3}\)
Vậy ta kết luận A < B