Evaluate the expression
\[
  \frac{121 \left( \frac{1}{13} - \frac{1}{17} \right) 
          + 169 \left( \frac{1}{17} - \frac{1}{11} \right) + 289 \left( \frac{1}{11} - \frac{1}{13} \right)}{
        11 \left( \frac{1}{13} - \frac{1}{17} \right) 
          + 13 \left( \frac{1}{17} - \frac{1}{11} \right) + 17 \left( \frac{1}{11} - \frac{1}{13} \right)} \, .
\]

Let's think step by step and output the final answer within \boxed{}.
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