We all know 1+1=2, so here is the prove and see if you guys know what'w wrong of it

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Let a=b=1
By formula
(a^2-b^2)=(a+b)(a-b)
Both sides divided by (a-b) which becomes
(a^2-b^2)/(a-b)=(a+b)(a-b)/(a-b)
Therefore (a^2-b^2)/(a-b)=(a+b)
Left hand side a^2-b^2 = 1x1-1x1=0
Right hand side a+b=1+1
by defination, 0/any number = 0
Therefore 0/(a-b)=0=1+1(Right hand side)
Hence 1+1=0 Proved!