The given expression is:
\[
\frac{-2 + \sqrt{5}}{8}
\]
Step 2: Check if the denominator can be rationalized
The denominator is \(8\), which is a rational number. Since there is no radical in the denominator, the expression is already in its simplest form with a rationalized denominator.
Step 3: Finalize the expression
No further simplification or rationalization is needed. The expression remains:
\[
\frac{-2 + \sqrt{5}}{8}
\]