\[\frac{x - 18\sqrt{x} + 81}{x - 81} = \frac{\left( \sqrt{x} - 9 \right)^{2}}{\left( \sqrt{x} - 9 \right)\left( \sqrt{x} + 9 \right)} =\]
\[= \frac{\sqrt{x} - 9}{\sqrt{x} + 9}\]