So sánh 2 biểu thức A = 10^2025 + 2/10^2025 − 1 và B = 10^2025/10^2025 − 3 .

Ta có: \(A = \frac{{{{10}^{2025}} + 2}}{{{{10}^{2025}} - 1}} = \frac{{{{10}^{2025}} - 1 + 3}}{{{{10}^{2025}} - 1}} = 1 + \frac{3}{{{{10}^{2025}} - 1}}\)

\(B = \frac{{{{10}^{2025}}}}{{{{10}^{2025}} - 3}} = \frac{{{{10}^{2025}} - 3 + 3}}{{{{10}^{2025}} - 3}} = 1 + \frac{3}{{{{10}^{2025}} - 3}}\)

So sánh: \({10^{2025}} - 1 > {10^{2025}} - 3\)

\(\frac{3}{{{{10}^{2025}} - 1}} < \frac{3}{{{{10}^{2025}} - 3}}\)

\(1 + \frac{3}{{{{10}^{2025}} - 1}} < \,\,1 + \frac{3}{{{{10}^{2025}} - 3}}\)

Vậy \(A < B\).