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\begin{equation*}
  L^*_e = \frac{r H_e (c + H_e)}{a H_e} \Bigl(1 - \frac{H_e}{k} \Bigr)
  = \frac{b c r (a b k - cd - dk)}{(ab - d)^2 k}.
\end{equation*}
\end{document}