$R\left(T\right)=R\left(T_0\right)\left(1+\alpha \Delta T\right)|:R\left(T_0\right)$

$\frac{R\left(T\right)}{R\left(T_0\right)}=1+\alpha \Delta T|-1$

$\frac{R\left(T\right)}{R\left(T_0\right)}-1=\alpha \Delta T|:\Delta T$

$\alpha =\frac{\frac{R\left(T\right)}{R\left(T_0\right)}-1}{\Delta T}$

$\alpha =\frac{\frac{R\left(T\right)}{R\left(T_0\right)}-1}{T-T_0}$