Why do we divide by slip in the Rotor equivalent circuit for an Induction motor?
R/s accounts for the change in rotor current and power with different values of slip. The power dissipated in R/s is the electrical power converted to heat in the rotor plus the electrical power converted to mechanical power. Separating R/s into R and R(1-s)/S separates the rotor losses from the mechanical power. You should probably find some other presentations that are similar to the one you linked. One of them may explain in a way that is easier for you to understand.