Giá trị biểu thức \(A = \frac{{{5^2} - 1}}{{{3^2} - 1}}:\frac{{{9^2} - 1}}{{{7^2} - 1}}:\frac{{{{13}^2} - 1}}{{{{11}^2} - 1}} :...:\frac{{{{55}^2} - 1}}{{{{53}^2} - 1}}\) là:

\(\begin{array}{*{20}{c}}{A = \frac{{{5^2} - 1}}{{{3^2} - 1}}:\frac{{{9^2} - 1}}{{{7^2} - 1}}  :\frac{{{{13}^2} - 1}}{{{{11}^2} - 1}}:...:\frac{{{{55}^2} - 1}}{{{{53}^2} - 1}}}\\\begin{array}{l} = \frac{{{5^2} - 1}}{{{3^2} - 1}} \cdot \frac{{{7^2} - 1}}{{{9^2} - 1}} \cdot \frac{{{{11}^2} - 1}}{{{{13}^2} - 1}}...\frac{{{{53}^2} - 1}}{{{{55}^2} - 1}}\\ = \frac{{4.6}}{{2.4}} \cdot \frac{{6.8}}{{8.10}} \cdot \frac{{10.12}}{{12.14}}...\frac{{52.54}}{{54.56}}\\ = \frac{6}{2} \cdot \frac{6}{{10}} \cdot \frac{{10}}{{14}}...\frac{{52}}{{56}}\\ = 3 \cdot \frac{6}{{56}} = \frac{9}{{28}}\end{array}\end{array}\)