((x-1)/(2x-4))+((x-2)/(3x))=1

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Solution for ((x-1)/(2x-4))+((x-2)/(3x))=1 equation: 


D( x )

3*x = 0

2*x-4 = 0

3*x = 0

3*x = 0

3*x = 0 // : 3

x = 0

2*x-4 = 0

2*x-4 = 0

2*x-4 = 0 // + 4

2*x = 4 // : 2

x = 4/2

x = 2

x in (-oo:0) U (0:2) U (2:+oo)

(x-1)/(2*x-4)+(x-2)/(3*x) = 1 // - 1

(x-1)/(2*x-4)+(x-2)/(3*x)-1 = 0

(3*x*(x-1))/(3*x*(2*x-4))+((x-2)*(2*x-4))/(3*x*(2*x-4))+(-1*3*x*(2*x-4))/(3*x*(2*x-4)) = 0

3*x*(x-1)+(x-2)*(2*x-4)-1*3*x*(2*x-4) = 0

5*x^2-6*x^2-11*x+12*x+8 = 0

x-x^2+8 = 0

x-x^2+8 = 0

x-x^2+8 = 0

DELTA = 1^2-(-1*4*8)

DELTA = 33

DELTA > 0

x = (33^(1/2)-1)/(-1*2) or x = (-33^(1/2)-1)/(-1*2)

x = (33^(1/2)-1)/(-2) or x = (33^(1/2)+1)/2

(x-((33^(1/2)-1)/(-2)))*(x-((33^(1/2)+1)/2)) = 0

((x-((33^(1/2)-1)/(-2)))*(x-((33^(1/2)+1)/2)))/(3*x*(2*x-4)) = 0

((x-((33^(1/2)-1)/(-2)))*(x-((33^(1/2)+1)/2)))/(3*x*(2*x-4)) = 0 // * 3*x*(2*x-4)

(x-((33^(1/2)-1)/(-2)))*(x-((33^(1/2)+1)/2)) = 0

( x-((33^(1/2)+1)/2) )

x-((33^(1/2)+1)/2) = 0 // + (33^(1/2)+1)/2

x = (33^(1/2)+1)/2

( x-((33^(1/2)-1)/(-2)) )

x-((33^(1/2)-1)/(-2)) = 0 // + (33^(1/2)-1)/(-2)

x = (33^(1/2)-1)/(-2)

x in { (33^(1/2)+1)/2, (33^(1/2)-1)/(-2) }

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