2-1/(x-1)=x

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


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

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

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

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

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

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

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

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

3*x-x^2-3 = 0

3*x-x^2-3 = 0

3*x-x^2-3 = 0

DELTA = 3^2-(-3*(-1)*4)

DELTA = -3

DELTA < 0

1 = 0

1/(x-1) = 0

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

1 = 0

x belongs to the empty set

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