Baker–Campbell–Hausdorff equation

[Franky4]

I have a question about Baker–Campbell–Hausdorff identity in QM: exp(X)*exp(Y) = exp(X + Y + [X,Y]/2)
I have exp(X + Y) where X and Y don't commute and want to try to write in multiplication form. Tried adding and subtracting commutator term: exp(X + Y + [X,Y]/2 - [X,Y]/2), but now I am not sure whether identity still holds: exp(X + Y + [X,Y]/2 - [X,Y]/2) =? exp(X + Y)*exp(- [X,Y]/2) .

 

[blue_leaf77]

Do you have further knowledge about [X,Y], i.e. whether it equals to another operator or just a number instead?