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

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


D( x )

1-x = 0

x = 0

1-x = 0

1-x = 0

1-x = 0 // - 1

-x = -1 // * -1

x = 1

x = 0

x = 0

x in (-oo:0) U (0:1) U (1:+oo)

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

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

3-(x/(1-x))-x^-1 = 0

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

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

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

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

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

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

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

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

DELTA = 0

x = -4/(-4*2)

x = 1/2 or x = 1/2

(x-1/2)^2 = 0

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

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

(x-1/2)^2 = 0

x-1/2 = 0 // + 1/2

x = 1/2

x in { 1/2, 1/2 }

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