2x/(x-3)-6/x=18/(x^2-3x)

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Solution for 2x/(x-3)-6/x=18/(x^2-3x) equation: 


D( x )

x^2-(3*x) = 0

x = 0

x-3 = 0

x^2-(3*x) = 0

x^2-(3*x) = 0

x^2-3*x = 0

x^2-3*x = 0

DELTA = (-3)^2-(0*1*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)+3)/(1*2) or x = (3-9^(1/2))/(1*2)

x = 3 or x = 0

x = 0

x = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:0) U (0:3) U (3:+oo)

(2*x)/(x-3)-(6/x) = 18/(x^2-(3*x)) // - 18/(x^2-(3*x))

(2*x)/(x-3)-(18/(x^2-(3*x)))-(6/x) = 0

(2*x)/(x-3)-18*(x^2-3*x)^-1-6*x^-1 = 0

(2*x)/(x-3)-18/(x^2-3*x)-6/x = 0

x^2-3*x = 0

x^2-3*x = 0

x*(x-3) = 0

x-3 = 0 // + 3

x = 3

x*(x-3) = 0

(2*x)/(x-3)-18/(x*(x-3))-6/x = 0

(2*x*x)/(x*(x-3))-18/(x*(x-3))+(-6*(x-3))/(x*(x-3)) = 0

2*x*x-6*(x-3)-18 = 0

2*x^2-6*x-18+18 = 0

2*x^2-6*x = 0

2*x^2-6*x = 0

2*x*(x-3) = 0

x-3 = 0 // + 3

x = 3

2*x*(x-3) = 0

(2*x*(x-3))/(x*(x-3)) = 0

(2*x*(x-3))/(x*(x-3)) = 0 // * x*(x-3)

2*x*(x-3) = 0

( 2*x )

2*x = 0 // : 2

x = 0

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 0} 

x in { 3} 

x belongs to the empty set

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