1. The problem statement, all variables and given/known data lim x --> 0 for the function sqrt((1/x^2)-(1/x)) - sqrt((1/x^2)-(1/x)) Analyze the cases x > 0 and x < 0 3. The attempt at a solution The solutions book simplifies the expression to 2x/(abs(x)*(sqrt(1+x)+sqrt(1-x))) I know how to evaluate the limit from here. But I'm wondering why did they only place the absolute value sign for the single x in the denominator that multiplies with this (sqrt(1+x)+sqrt(1-x)) expression. Why isn't the absolute value sign around every single x? The answer is that the limit doesnt exist.