when we find a limit for an undefined point on a curve , X^2 - 1 / x - 1 at x = 1 for instance we reshape the equation without actually changing anything to find the limit at this point . why cant we do that to define the point on the function ? i mean clearly if we say F(x) = x^2 - 1 / X - 1 we can reshape it by doing F(x) = (x-1) ( X+1 ) / x-1 which is equal to x +1 it only works for the limit , why doesn't it work for defining the function at this point ? are we only limited to using the shape of the equation that the function is defined by ? would changing the shape of the function ( the way we express it ) * even though it changes nothing mathematically * change the function ?