1. **State the problem:** Simplify the expression $$\frac{xy + x^2y^2}{xy}.$$\n\n2. **Recall the rule:** When dividing a sum by a term, you can split the fraction as $$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}.$$\n\n3. **Apply the rule:**\n$$\frac{xy + x^2y^2}{xy} = \frac{xy}{xy} + \frac{x^2y^2}{xy}.$$\n\n4. **Simplify each term:**\n- For $$\frac{xy}{xy}$$, numerator and denominator are the same, so it equals 1.\n- For $$\frac{x^2y^2}{xy}$$, divide powers of the same base by subtracting exponents: $$x^{2-1} y^{2-1} = xy.$$\n\n5. **Write the simplified expression:**\n$$1 + xy.$$\n\n**Final answer:** $$1 + xy.$$