1. **State the problem:** Simplify the expression $\frac{7x^2}{2x}$.\n\n2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $\frac{x^a}{x^b} = x^{a-b}$.\n\n3. **Apply the rule to the variables:** $\frac{7x^2}{2x} = \frac{7}{2} \cdot \frac{x^2}{x^1} = \frac{7}{2} x^{2-1} = \frac{7}{2} x^1 = \frac{7}{2} x$.\n\n4. **Show intermediate cancellation:** $\frac{7\cancel{x^2}}{2\cancel{x}} = \frac{7}{2} x$.\n\n5. **Final answer:** $\frac{7}{2} x$.