Determine which one of the following two numbers is greater: $\frac{2.00013579}{1.00013579^2+2.00013579}$ or $\frac{2.0002468}{1.0002468^2 + 2.0002468}$.
How can I do this without a calculator? I tried comparing the numerator to the numerator, and the denominator to the denominator, but that did not work. I tried seeing whether the squares would change very little since they were really close to $1$, but I couldn't form any solid reasoning.
Thanks!