solve :`(|x-1|)/(x+1)lt1`

Answer

N/a

Explanation

`(|x-1|)/(x+1)lt1`
`rArr (|x-1|)/(x+1)-1lt0`
`rArr (|x-1|-x-1)/(x=1)lt0`
If `x-1ge0 rArr x ge 1`
Then `|x-1| - x-1`
`:. (|x-1|-x-1)/(x+1)lt0`
`rArr (|x-1|-x-1)/(x+1)lt 0 `
`rArr (-2)/ (x+1) lt0`
`rArr x+1 gt 0`
`rArr x gt -1 `
But x `ge` 1
`:. xin [1, infty`) ...(1)
If x-1 lt` rArr` xlt1
Then `|x -1| = -(x-1)`
`:. (|x-1|-x-1)/(x+1)lt 0`
`rArr (-(x-1)-x-1)/(x+1) lt0`
`rArr (-2x)/(x+1)lt 0`
`rArr (x)/(x+1) gt 0`
`rArr (xgt0, x+1gt 0) or ( xlt 0, x+1lt0)`
`rArr (x gt 0, x gt -1) or (x lt 0, x lt -1)` ltbgt `rArr x gt 0 or x lt -1`
But `x lt 1`
`:.` x`in` (-`infty`, -1) cup (0,1) " " ...(2)
From eqs . (1) and (2)
e `in` [1, `infty` )`cup` (-`infty` , -1)`cup` (0, 1)
`rArr x in (-infty ,-1) cup (0, infty)`.