Absolute Value $|1-(1/x)| = |(1/x)-1|$

Question

Can someone please explain to me how: $$|1-(1/x)| = |(1/x)-1|$$ Im working on a limit problem in my calculus book and I cant seem to understand how they reversed this and it equals the same thing.

Thanks!

Answer 1

This is an identity, as has been mentioned already. In general, if $\vert x\vert =\vert y\vert$ then $x=\pm y$. You can see this geometrically or by considering cases, but perhaps the easiest way is to note that $\vert x\vert =\sqrt{x^{2}}$.