Are they the same function? $y = x^2/x$ and $y = x$ Are they the same function?
$$y=\frac{x^2}{x}$$
and
$$y=x$$
For the first function, if we don't divide both the numerator and the denominator by x, then the domain of it is the real line except the point x = 0, which is different from the domain of the second function. 

The are not the same function, since they have different domains.
For two function to be the same they should have the same domain and the same mapping rules.
