Absolute Value Algebra with inverses I noticed the following equality in some material regarding limits and infinite series. 
$$ \left |\frac{x}{x+1} - 1 \right| = \left |\frac{-1}{x+1} \right| $$
And I'm honestly stumped (and slightly ashamed) on how to algebraically go from the lefthand side to the righthand side. Any pointers?
Thanks!

It's just a little bit of algebra to get there.
\begin{align*}
\left|\frac{x}{x+1} -1\right| &= \left|\frac{x}{x+1} - \frac{x+1}{x+1}\right| \\ &= \left|\frac{x-x-1}{x+1}\right| \\ &= \left|\frac{-1}{x+1}\right|
\end{align*}
I hope that helps.
