Prove that `sqrt(x^2+2x+1)-sqrt(x^2-2x+1)={-2, x<-1 2x,-1lt=xlt=1 2,x >1`

Explanation

`sqrt(x^(2)+2x+1)-sqrt(x^(2)-2x+1)`
`=sqrt((x+1)^(2))-sqrt((x-1)^(2))`
`=|x+1|-|x-1|`
`= {(-x-1-(1-x)", "x lt -1),(x+1-(1-x)", "-1le x le1),(x+1-(x-1)", "x gt1):}`
`= {(-2", "x lt -1),(2x","-1le x le1),(2", "x gt1):}`