Final answer:
Defending against simultaneous attacks was challenging for the Western Roman Empire due to a vulnerable frontier, under-equipped armies, and the well-organized nature of barbarian invasions. Contrastingly, the Eastern Empire faced fewer threats and was better defended, which contributed to its longevity even as the West declined.
Step-by-step explanation:
Defending against multiple groups attacking the Western Roman Empire simultaneously would be significantly challenging due to several key factors. First, the Western Roman Empire had a longer frontier which increased vulnerability to invasions. Additionally, the Western Roman armies were under-funded, under-manned, and vulnerable, leading to a vicious cycle of lost land, lost revenue, and poor military performance. Concurrent attacks by well-organized barbarian groups exceeded the logistical and military capabilities of the Western Romans, resulting in losses that the empire was ill-equipped to recuperate from.
The Eastern Roman Empire, or Byzantium, on the other hand, faced less pressure during this period. The eastern regions enjoyed a simpler frontier defense, greater urbanization, and better military funding, which contributed to its resilience against similar threats. Moreover, the barbarians tended to migrate west rather than east, and Persia did not launch major invasions during the critical period, which helped preserve the Eastern Roman Empire from succumbing to the same fate as the West.