Evaluate the limit: $\lim _{n \rightarrow \infty} \frac{A+e^{n x}}{x+A e^{n x}}$
- A$\frac{A}{x}$,when $x < 0$
- B$1$,when $x > 0$
- C$0$,when $\forall x \in \mathbb{R}$
- D$A$,when $x = 0$
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