Art of Electronics - Zener Diode Example
$$ ΔV_{out} = { R_{dyn}ΔI} = \frac{R_{dyn}}{R} (ΔV_{in} - ΔV_{out}) $$

$$ ΔV_{out} + \frac{R_{dyn}}{R} ΔV_{out} = \frac{R_{dyn}}{R} ΔV_{in} $$

$$ ΔV_{out} \cdot (1 + \frac{R_{dyn}}{R}) = \frac{R_{dyn}}{R} ΔV_{in} $$

$$ ΔV_{out} = \frac{\frac{R_{dyn}}{R}}{1 + \frac{R_{dyn}}{R}} ΔV_{in} \| \cdot \frac{R}{R}$$

$$ ΔV_{out} = \frac{R_{dyn}}{R + R_{dyn}} ΔV_{in} $$