हल कीजिए - `(|x-1|)/(x+1) lt 1`

Explanation

`(|x-1|)/(x+1) lt 1`
`rArr" "(|x-1|)/(x+1)-1 lt 0`
`rArr" "(|x-1|-x-1)/(x+1) lt 0`
यदि `x - 1 ge 0` अर्थात `x ge 1`
तो `|x-1| = x - 1`
`therefore" "(|x-1|-x-1)/(x+1) lt 0`
`rArr" "(x-1-x-1)/(x+1) lt 0`
`rArr" "(-2)/(x+1) lt 0`
`rArr" "x + 1 gt 0`
`rArr" "x gt -1`
परन्तु `x ge 1`
`therefore" "x in [1, oo)" "...(1)`
यदि `x - 1 lt 0` अर्थात `x lt 1`
तो `|x-1| = - (x-1)`
`therefore" "(|x-1|-x-1)/(x+1) lt 0`
`rArr" "(-(x-1)-x-1)/(x+1) lt 0`
`rArr" "(-2x)/(x+1) lt 0`
`rArr" "(x)/(x+1) gt 0`
`rArr" "(x gt 0, x + 1 gt 0)` या `(x lt 0, x + 1 lt 0)`
`rArr" "(x gt 0, x gt -1)` या `(x lt 0, x lt -1)`
`rArr" "x gt 0` या `x lt -1`
परन्तु `x lt 1`
`therefore" "x in (-oo, -1)uu(0, 1)" "...(2)`
(1) और (2) से
`x in [1, oo)uu(-oo, -1)uu(0, 1)`
`rArr" "x in (-oo, -1)uu(0, oo)`