1. **State the problem:** Simplify the expression $\frac{2x^2}{2x}$. 2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$. Also, common factors in numerator and denominator can be canceled. 3. **Apply the rule to the coefficients:** $\frac{\cancel{2}x^2}{\cancel{2}x} = \frac{x^2}{x}$. 4. **Apply the rule to the variables:** $\frac{x^2}{x} = x^{2-1} = x^1 = x$. 5. **Final answer:** $x$.