FORMULA - Remove A1 content from A2

[seanjacob]

Example -

A1
dog

A2
cat;dog;bat;rat;

B1
red

B2
blue;green,red;pink;

-----

I would like a formula that is able to remove "dog;" from A2 and when dragged down also be able to remove "red;" from B2.

My go at the formula

=IF(ISNUMBER(SEARCH(A1,A2)),A1-A2)