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Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1)...

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

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`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)","-1 lex le 1),(x+1-(x-1)"," x gt1):}={{:(-2","x lt-1),(2x ","-1 le x le1),(2 "," x gt 1):}`
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