Remove Duplicates from 2 columns then auto sort

Hello,

I am trying to remove duplicates from 2 columns automatically without using a macro. I have a formula that does this but it replaces the duplicates with blank cells. How would I remove these blanks? I want this to automatically take place whenever the document is opened. I was thinking if I could automatically sort, the blanks would just get moved to the bottom but I am not sure how to do this. I have attached what I have done so far.

Thank you!