にかまけて means "being so taken up with X that you neglect something else". It follows a noun – work, play, being busy – and the second half names what was neglected, often with , or a plain negative.
、。
I was so caught up in work that I never made time for my family.
、。
He's been so busy having fun that he hasn't done any homework at all.
、。
I let being busy get in the way and didn't keep in touch with friends.
It always criticises, either someone else or yourself looking back. The thing you were busy with can be perfectly reasonable – work, childcare – but the pattern blames you for what it pushed aside.
、。
Don't use being busy as a reason to neglect your health.
、。
We were so focused on short-term profit that we never made a long-term plan.
にかまけて or に夢中で
says only that you were absorbed in something, and it can be happy. にかまけて always has a casualty: something else was neglected.
、。
I was so absorbed in the game that I lost track of time.
、。
I let games take over and neglected my studies.
にかまけて is a little bookish. In casual speech the same complaint is usually made with .
、。
He does nothing but play and hasn't done any of his homework.
Lingaku