A transmission device, for a motor vehicle, with at least two drive output shafts and two multi-shaft planetary gearsets in active connection with one another. A shaft of a planetary gearset is actively connected with an output shaft and is shifted, between first and second power paths, such that in the first power path, torque of an electric machine is transmitted in equal parts and with the same sign to the output shafts, and in the second power path, torque is transmitted in equal parts but with different signs. One of the two planetary gearsets is made as a four-shaft, reduced coupling transmission with two sun gears and a common planetary gear carrier with radially inner and outer planetary gears that mesh with one another, and which are engaged, on the one hand, with the sun gears and, on the other hand, with a rotationally fixed ring gear.