Let's rewrite the expression as

So, if  , you may divide both sides by
, you may divide both sides by  , the equation becomes
, the equation becomes  , and the only solution is
, and the only solution is  , which means that this is not an identity (an indentity is tautologically true, no matter the value of x).
, which means that this is not an identity (an indentity is tautologically true, no matter the value of x).
If instead  , you are multiplying both sides by zero, so the equation becomes
, you are multiplying both sides by zero, so the equation becomes

So, it doesn't matter which value for x you choose, because you will always end up with  , which is obviously always true.
, which is obviously always true.