[Cronos]

Your point

(a+b)=(a-b)/(a-b)=1

Then means (by resubstituting a=b=1)

1+1=(1-1)/(1-1)=1
2 = 0/0 = 1

You can't divide by 0.

[notfornothing]

You can't divide by 0.

Sure you can, and this is a meaningful result. 0/0 (ie "indeterminate") is logically different from, say [a positive real]/0 (eg 1/0 = "undefined".) 0/0 could be anything - 1, 3.5, pi, you name it. The point is that on a meaningfully infinite scale, 1 and 2 (or any two other positive reals) are exactly the same.