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## Homework Statement

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

## 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.

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