9/(6x-9)=x/(2x-3)-1/3

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Solution for 9/(6x-9)=x/(2x-3)-1/3 equation: 


D( x )

6*x-9 = 0

2*x-3 = 0

6*x-9 = 0

6*x-9 = 0

6*x-9 = 0 // + 9

6*x = 9 // : 6

x = 9/6

x = 3/2

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

x in (-oo:3/2) U (3/2:+oo)

9/(6*x-9) = x/(2*x-3)-(1/3) // - x/(2*x-3)-(1/3)

9/(6*x-9)-(x/(2*x-3))+1/3 = 0

9/(6*x-9)+(-1*x)/(2*x-3)+1/3 = 0

(3*9*(2*x-3))/(3*(6*x-9)*(2*x-3))+(-1*3*x*(6*x-9))/(3*(6*x-9)*(2*x-3))+(1*(6*x-9)*(2*x-3))/(3*(6*x-9)*(2*x-3)) = 0

3*9*(2*x-3)-1*3*x*(6*x-9)+1*(6*x-9)*(2*x-3) = 0

12*x^2-18*x^2+81*x-36*x-81+27 = 0

45*x-6*x^2-54 = 0

45*x-6*x^2-54 = 0

3*(15*x-2*x^2-18) = 0

15*x-2*x^2-18 = 0

DELTA = 15^2-(-18*(-2)*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)-15)/(-2*2) or x = (-81^(1/2)-15)/(-2*2)

x = 3/2 or x = 6

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

(3*(x-3/2)*(x-6))/(3*(6*x-9)*(2*x-3)) = 0

(3*(x-3/2)*(x-6))/(3*(6*x-9)*(2*x-3)) = 0 // * 3*(6*x-9)*(2*x-3)

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

( 3 )

3 = 0

x belongs to the empty set

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

( x-6 )

x-6 = 0 // + 6

x = 6

x in { 3/2} 

x = 6

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