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

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


D( x )

3*x-1 = 0

3-x = 0

3*x-1 = 0

3*x-1 = 0

3*x-1 = 0 // + 1

3*x = 1 // : 3

x = 1/3

3-x = 0

3-x = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

x in (-oo:1/3) U (1/3:3) U (3:+oo)

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

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

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

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

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

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

5-5*x^2 = 0

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

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

5-5*x^2 = 0

-5*x^2 = -5 // : -5

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in { 1, -1 }

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