1. We are given two natural numbers where the difference between the larger and smaller number is 1. 2. Let the smaller number be $s$. Then the larger number is $s+1$. 3. The sum of thrice the reciprocal of the smaller number and twice the reciprocal of the larger number is given as $\frac{3}{2}$. 4. Writing this as an equation in $s$, we have: $$3 \times \frac{1}{s} + 2 \times \frac{1}{s+1} = \frac{3}{2}$$ 5. Simplifying, the equation is: $$\frac{3}{s} + \frac{2}{s+1} = \frac{3}{2}$$ This is the required equation in $s$ as requested.