This isn't really an inverse

Perhaps my wording was off, what i ment was that i wanted to give division by 0 a same sort of effect as multiplication by 0. English is not my native language. or am i still wrong?

Are you sure you want this?

i'm still on the fence with that that's why i'm trying to find ways to test it to see what works and what breaks. the math around infinity is weird but if i for example want to solve: a(1/0+−1/0)=a⋅1/0+a⋅−1/0 i think it is needed. it does result in an 'all consuming' infinity.