1. **State the problem:** Simplify the expression $$\frac{f-1}{e g} \div \frac{f g}{g+2} = \frac{g}{g}$$. 2. **Recall the division of fractions rule:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{f-1}{e g} \div \frac{f g}{g+2} = \frac{f-1}{e g} \times \frac{g+2}{f g}$$. 3. **Multiply the fractions:** $$= \frac{(f-1)(g+2)}{e g \cdot f g} = \frac{(f-1)(g+2)}{e f g^2}$$. 4. **Simplify the right side:** The right side is $$\frac{g}{g}$$, which simplifies to 1 (assuming $$g \neq 0$$). 5. **Set the equation:** $$\frac{(f-1)(g+2)}{e f g^2} = 1$$. 6. **Solve for the relationship:** Multiply both sides by $$e f g^2$$: $$(f-1)(g+2) = e f g^2$$. 7. **Interpretation:** This equation relates the variables $$e, f, g$$. Without additional information, this is the simplified form. **Final answer:** $$\boxed{\frac{f-1}{e g} \div \frac{f g}{g+2} = \frac{(f-1)(g+2)}{e f g^2} = 1}$$