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

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


D( x )

4/x-2 = 0

x = 0

4/x-2 = 0

4/x-2 = 0

4*x^-1 = 2 // : 4

x^-1 = 1/2

-1 < 0

1/(x^1) = 1/2 // * x^1

1 = 1/2*x^1 // : 1/2

2 = x^1

x = 2

x = 0

x = 0

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

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

(3/x)/(4/x-2)-x = 0

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

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

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

2*x+3*x^-1-4 = 0

2*x+3*x^-1-4 = 0

2*x^1+3*x^-1-4*x^0 = 0

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

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

x^1

2*x^2-4*x+3 = 0

2*x^2-4*x+3 = 0

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

DELTA = -8

DELTA < 0

x in { } 

1 = 0

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

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

1 = 0

x belongs to the empty set

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