Limit of a indeterminate function is always can be calculated?

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In class, a teacher made the following statement:

Whenever the limit of a real function of a real variable gives $\frac{0}{0}$ for $x \to a$, the limit can be calculated (via L'Hopital for example). I haven't seen any books claiming this (or giving a counterexample).

Does anyone know how to prove this statement or give a counterexample?