Let's say I have following expression
$$ \alpha = \frac{R_s + R_r\cdot\frac{L^2_h}{L^2_r}}{L_{s\sigma} + \frac{L_h}{L_r}\cdot L_{r\sigma}} $$
where following relationships holds $$ L_s = L_{s\sigma} + L_h $$ $$ L_r = L_{r\sigma} + L_h $$
I have been looking for a way how to express the $\alpha$ with usage of following expressions
$$R_S = R_s$$ $$R_R = R_r\cdot\frac{L^2_s}{L^2_h}$$ $$L_L = L_{r\sigma}\cdot\frac{L^2_s}{L^2_h} + L_{s\sigma}\cdot\frac{L_s}{L_h}$$ $$L_M = L_s$$