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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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To prove the equation \[ \sqrt{x^2 + 2x + 1} - \sqrt{x^2 - 2x + 1} = \begin{cases} -2 & \text{if } x < -1 \\ 2x & \text{if } -1 \leq x \leq 1 \\ 2 & \text{if } x > 1 ...
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