1. **Problem:** Solve the variable separable differential equation $y' = \frac{x^{-2}}{x^{-2}}$ passing through the point $(3, 2)$. 2. **Rewrite the equation:** Since both numerator and denominator are $x^{-2}$, simplify: $$y' = \frac{x^{-2}}{x^{-2}} = 1$$ This means: $$\frac{dy}{dx} = 1$$ 3. **Separate variables:** The equation is already separated, so integrate both sides with respect to $x$: $$\int dy = \int 1 \, dx$$ 4. **Integrate:** $$y = x + C$$ 5. **Use initial condition $(3, 2)$ to find $C$:** $$2 = 3 + C \implies C = 2 - 3 = -1$$ 6. **Final solution:** $$\boxed{y = x - 1}$$ This is the explicit solution passing through $(3, 2)$.