TITLE: What is $\lim_{x \to 0} \frac{|x+1|+|x-1|-2}{|x+1|+|x-1|-2}$?
QUESTION [5 upvotes]: $\displaystyle \lim_{x \to 0} \frac{|x+1|+|x-1|-2}{|x+1|+|x-1|-2}$ 
If $x \to 0$, then it does not matter the value when $x=0$, then would not it be just equivalent to $\displaystyle \lim_{x \to 0} 1$ which is equal to $1$? 
But Wolfram´s answer is: Limit does not exist on the real line, there are infinitely many singularities in every neighborhood of $0$.
Wolfram
Is Wolfram wrong?

REPLY [6 votes]: When $x$ is near $0$ we have $|x+1|+|x-1|-2=(x+1)+(1-x) -2=0$. So the ratio is undefined for all $x$ near $0$.