\[\frac{1}{\sqrt{26} - 1} =\]
\[= \frac{\sqrt{26} + 1}{\left( \sqrt{26} - 1 \right)\left( \sqrt{26} + 1 \right)} =\]
\[= \frac{\sqrt{26} + 1}{26 - 1} = \frac{\sqrt{26} + 1}{25}\]