why it is not continuous for a absolute value division?

Question

the question is : is y=|x-1|/(x-1）continuous on (-infi, +infi):

I am wondering why this equation is not continuous when x = 1

I think when x=1, y will be 1

Answer 1

$\lim_{x\to 1^+}\frac{|x-1|}{x-1}=\lim_{x\to 1^+}\frac{x-1}{x-1}=1\color{red}{\neq}\lim_{x\to 1^-}\frac{|x-1|}{x-1}=\lim_{x\to 1^-}\frac{-(x-1)}{x-1}=-1$