。
She shared the cake with me.
Literal
She [topic-は] me [with-と] cake [object-を] shared.
分け合う is a compound verb: 分ける ('to divide, to split') + 合う ('to do mutually'). The ~合う suffix on a verb stem creates a reciprocal sense — actions performed jointly or against each other. Other examples: 助け合う ('help each other'), 殴り合う ('hit each other'). With 分ける, the result is 'split [it] between us' — emphasizing the mutuality of the sharing. Plain 分ける would just describe the dividing; 分け合う brings the joint participation into focus.