Prove that
`sqrt(x^2+2x+1)-sqrt(x^2-2x+1)`=
`{-2 , x<-1,
2x, -1lt=xlt=1
2, x >1}`
Text Solution
Verified by Experts
`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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