To perform the operation on the expression \(\frac{3\sqrt{5} - 7}{11}\) and ensure the denominator is rationalized (if necessary), we can start by simply rewriting it since the denominator, in this case, is already rational.
Thus, the expression is already in a simplified form:
\[ \frac{3\sqrt{5} - 7}{11} \]
Since there's no further operation to perform and the denominator does not involve a square root or any irrational number, there's no need for further rationalization.
The final answer is:
\[ \frac{3\sqrt{5} - 7}{11} \]
This expression is in its exact form and cannot be simplified further.