1/0 = 1/0 is it a true sentence? I have a doubt. I ask for help.
The Principle of Identity ("Anything is equal to itself") allows us to state, 
  without assigning any meaning to 1/0, that "1/0 = 1/0" is it a true sentence?
Or, in that case, would it be better to say that "1/0 = 1/0" is it an open sentence of type "x = x"?
 A: No, it does not make sense (unless you are working with the extended real numbers, for example). You cannot apply the principle "anything is equal to itself" in this case, because $1/0$ is undefined, so there is no applicable "thing" or "self".
On the other hand, we can compare strings of text, so it is quite fine to assert the equality that
$$\text{"1/0" = "1/0"}$$
in the same way that "hello" = "hello".
A: $1/0$, interpreted as the evaluation of real number division with numerator $1$ and denominator $0$, is a grammatical error, since this pair of numbers is not in the domain of division.
Anything you say involving $1/0$ as a subexpression is therefore grammatically incorrect.
Trying to ascribing meaning to something despite grammatical errors is dangerous business. Usually, you can only get away with doing so when what you're really doing is making some implicit additions or corrections to remove the grammatical error (e.g. when facing $\frac{1}{x}$ in a setting where "$x$ is a real variable", to change the premise to "$x$ is a nonzero real variable").
There aren't many use cases where you can do that with $1/0$ as interpreted above — they mainly happen in settings where you would already know how to make sense of it, such as "I mean to do arithmetic in the real projective line".
A: This principle of $x=x$ only applies to actual "things" ie. $\mathbb{R}$ or $\mathbb{Z}$ or any other defined ring where it applies by definition. Because $\frac{1}{0}$ isn't defined (or rather is undefined by definition), we can't apply a property to it. Similarly to the way that we can't say $\left(\frac{1}{0}\right)^0 = 1$ or that $\left(\frac{1}{0}\right)^{-1} = \frac{0}{1}$
A: Standard first-order logic gives you no alternative: if you want a function symbol for division, then it must denote a total function and then $1/0 = 1/0$ has to be true. This offends a great number of people and so there is a lot of literature on logics that try to fit more nicely with human expectations about undefined terms. E.g., free logic. However there is no generally accepted solution and the standard first-order logic viewpoint wins for many people on the grounds of simplicity.
