Simplify the following expression: $$ \frac{\sqrt{x + x^2 + 1}}{x - 1} $$

The given expression is:

\[ \frac{\sqrt{x + x^2 + 1}}{x - 1} \]

This expression cannot be simplified further without additional context or constraints on the variable 'x'. It is already in its simplest form as a rational function involving a square root.

Answer:
\[ \frac{\sqrt{x^2 + x + 1}}{x - 1} \]