This is the adverb: in a way that cannot be separated. It describes how two or more things are joined, and it almost always sits right in front of a word like linked, bound, tied, connected, or joined. 'The two problems are indivisibly linked.' 'Her name is indivisibly bound up with the movement she started.' That is nearly the whole story of how the word behaves — it is a modifier looking for exactly that kind of verb. It is formal and rather literary; you would find it in an essay, a judgement, or a serious newspaper column, not in conversation. In ordinary speech people say 'you can't separate them' or 'they go together'. Some writers prefer inseparably in the same slot, and it sounds a little less stiff. Because the word is heavy, using it makes a strong claim: you are saying the connection is not merely close but impossible to undo. Use it when you mean that, and reach for closely or firmly when you do not.

不可分割地、密不可分地。幾乎都跟 linked / bound / connected 這類字連用，屬於書面正式用法。