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

1 Answer
Nov 1, 2015

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