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

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


D( x )

x = 0

3*x-2 = 0

x = 0

x = 0

3*x-2 = 0

3*x-2 = 0

3*x-2 = 0 // + 2

3*x = 2 // : 3

x = 2/3

x in (-oo:0) U (0:2/3) U (2/3:+oo)

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

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

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

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

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

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

x^2-2*m*x-6*x+4 = 0

x^2-2*m*x-6*x+4 = 0

x^2-6*x+4 = 0

DELTA = (-6)^2-(1*4*4)

DELTA = 20

DELTA > 0

x = (20^(1/2)+6)/(1*2) or x = (6-20^(1/2))/(1*2)

x = (2*5^(1/2)+6)/2 or x = (6-2*5^(1/2))/2

(x-((6-2*5^(1/2))/2))*(x-((2*5^(1/2)+6)/2)) = 0

((x-((6-2*5^(1/2))/2))*(x-((2*5^(1/2)+6)/2)))/(x*(3*x-2)) = 0

((x-((6-2*5^(1/2))/2))*(x-((2*5^(1/2)+6)/2)))/(x*(3*x-2)) = 0 // * x*(3*x-2)

(x-((6-2*5^(1/2))/2))*(x-((2*5^(1/2)+6)/2)) = 0

( x-((2*5^(1/2)+6)/2) )

x-((2*5^(1/2)+6)/2) = 0 // + (2*5^(1/2)+6)/2

x = (2*5^(1/2)+6)/2

( x-((6-2*5^(1/2))/2) )

x-((6-2*5^(1/2))/2) = 0 // + (6-2*5^(1/2))/2

x = (6-2*5^(1/2))/2

x in { (2*5^(1/2)+6)/2, (6-2*5^(1/2))/2 }

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