Question

For what `x` is `(3x)/(x+3)>3/(x-2)`?

Answer 1

The answer is `x > 2 " or " x < 3/2`

Explanation:

Note that
`(3x)/(x+3)>3/(x-2)`
`implies 3x*(x-2)> (x-2)* (x+3 )`
`implies 3x^2-6x > x^2+x-6`
`implies 2x^2 -7x +6 >0`
`implies 2 x^2 - 4x -3x +6 >0`
`implies 2x*(x-2) -3 (x-2)>0`
`implies( 2x - 3 )( x - 2 )>0`
`implies x > 2 " or " x < 3/2`