I asked a question here the other day and one of the steps in the answer I encountered was: $\left|x-1+\frac 1{1+x}-\left(y-1+\frac 1{1+y}\right)\right|\leq 2|x-y|$
when $x,y\ge0$
I can't seem to figure out why this is true.. Cans someone help me out?
Thanks :)