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Solve (x-2)/(x+2)gt(2x-3)/(4x-1)...

Solve `(x-2)/(x+2)gt(2x-3)/(4x-1)`

Text Solution

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`(x-2)/(x+2) gt (2x-3)/(4x-1)`
or `((x-2)(4x-1)-(x+2)(2x-3))/((x+2)(4x-1)) gt 0`
or `(4x^(2)-9x+2-2x^(2)-x+6)/((x+2)(4x-1)) gt 0`
or `(x^(2)-5x+4)/((x+2)(4x-1)) gt 0`
or `((x-1)(x-4))/((x+2)(4x-1)) gt 0`

`implies x in (-oo, -2) cup ((1)/(4),1) 1 cup (4, oo)`
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