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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 lt -1 ),(2x ","-1 le x le1),(2 "," x gt1):}`

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