(3x-4)/(1-2x)=(x+2)/(x-8)

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Solution for (3x-4)/(1-2x)=(x+2)/(x-8) equation: 


D( x )

1-(2*x) = 0

x-8 = 0

1-(2*x) = 0

1-(2*x) = 0

1-2*x = 0

1-2*x = 0 // - 1

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

x = -1/(-2)

x = 1/2

x-8 = 0

x-8 = 0

x-8 = 0 // + 8

x = 8

x in (-oo:1/2) U (1/2:8) U (8:+oo)

(3*x-4)/(1-(2*x)) = (x+2)/(x-8) // - (x+2)/(x-8)

(3*x-4)/(1-(2*x))-((x+2)/(x-8)) = 0

(3*x-4)/(1-2*x)-((x+2)/(x-8)) = 0

(3*x-4)/(1-2*x)+(-1*(x+2))/(x-8) = 0

((3*x-4)*(x-8))/((1-2*x)*(x-8))+(-1*(x+2)*(1-2*x))/((1-2*x)*(x-8)) = 0

(3*x-4)*(x-8)-1*(x+2)*(1-2*x) = 0

5*x^2-25*x+30 = 0

5*x^2-25*x+30 = 0

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

x^2-5*x+6 = 0

DELTA = (-5)^2-(1*4*6)

DELTA = 1

DELTA > 0

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

x = 3 or x = 2

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

(5*(x-2)*(x-3))/((1-2*x)*(x-8)) = 0

(5*(x-2)*(x-3))/((1-2*x)*(x-8)) = 0 // * (1-2*x)*(x-8)

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

( x-2 )

x-2 = 0 // + 2

x = 2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 2, 3 }

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