Simplify the following: $$\frac{x^{3} \cdot x^m}{x^{m+2}}$$

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Use the exponent rules as follows:

$$\frac{x^{3} \cdot x^m}{x^{m+2}}$$ $$=\frac{x^{3+m}}{x^{m+2}}$$ $$=x^{3+m-(m+2)}$$ $$=x^1$$ $$=\boxed{x}$$