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Solve (|x-1|)/(x+2) gt 1...

Solve `(|x-1|)/(x+2) gt 1`

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Verified by Experts

The correct Answer is:
`x in (-2 ,-1/2)`
`(|x-1|)/(x+2)gt1` ,
`rArr (|x-1|-(x+2))/(x+2)gt0`
Case I when `x ge1`
`((x+1)-(x+2))/(x+2)gt 0 `
Hence `x lt -2 `which is not possible as `x gt 1`
CaseII when `x lt 1`
`rArr ((1-x)-(x+2))/((x+2)) gt0 `
or`(-1-2x)/(x+2) gt 0 `
`or (2x+1)/((x+2)) lt 0 `
`rArr x in (-2 , 1/2 ) (as x lt1)`
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