How can you check by calculation whether the combination of an articulated motor vehicle (semitrailer load = vertical load) exceeds the permissible total mass of the combination of vehicles?

Your answer is correct. To check if an articulated vehicle combination exceeds the permissible total mass, you add the permissible total mass of the truck tractor to the permissible total mass of the semitrailer, then subtract the vertical load (the weight that the semitrailer exerts vertically on the truck tractor). This calculation accounts for the actual load distribution between the two parts, ensuring you do not overestimate the allowed combined mass. Simply adding the total masses without subtracting the vertical load would ignore this shared load, potentially leading to an incorrect total weight. Understanding this helps ensure compliance with German traffic regulations regarding vehicle weight limits.