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Solve `(x-2)/(x+5)gt2.`

Answer» We have `(x-2)/(x+5)gt2`
`rArr (x-2)/(x+5)-2gt0`
`rArr(x-2-2x-10)/(x+5)gt0`
`rArr (-(x+12))/(x+5)gt0` `rArr (x+12)/(x+5)lt0` [on mutipling both sides by -1].
`therefore " either "(x+12lt0 andx+5lgt0)or(x+12gt0andx+5lt0)`.
Case I When `x+12lt0andx+5gt0`.
In this case, `x+12lt0andx+5gt0`.
`rArr xlt-12andxgt-5`
`rArr -5ltxlt-12, " which is impossible " " "[therefore-12lt-5]`
Case II when `x+12gt0andx+5lt0`.
In this case, `x+12gt0andx+5lt0`.
`rArrxgt-12 andxlt-5`
`rArr -12ltxlt-5rArrx in(-12-5)`.
`therefore` solution set`=(-12-5)`.


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