How did western industrial powers gain global empires?

the right answer for the question that is being asked and shown above is that: "their policy of "divide and rule" pitted political groups against each other to keep any one group from becoming too powerful.  " the  participant in european imperialism is being described below is that  their policy of "divide and rule" pitted political groups against each other to keep any one group from becoming too powerful. 

the western roman empire flourished, but the eastern portion of the empire struggled.