These look almost the same, but they are different constructs. \code{where} is bound to the pattern matching \code{f x =} and may also have access to parts of a function that are not syntactically expressions, e.g.:
\begin{haskellcode}
f x
  | cond1 x   = a
  | cond2 x   = g a
  | otherwise = f (h x a)
  where
    a = w x
\end{haskellcode}
While that is not possible with \code{let}, which is an actual expression and can be used whenever expressions are allowed (e.g. inside \emph{Monads}, we'll know more about these in a few weeks).
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There are a few more intricacies, but most of the time this is just style consideration:\\ \url{https://wiki.haskell.org/Let_vs._Where}
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How would we have to rewrite the function in order to use \code{let}?