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

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

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Answer 1 · 2015-11-01T07:24:15

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#

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

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