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

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


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

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

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

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

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

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

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

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

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

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

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

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

DELTA = 25

DELTA > 0

x = (25^(1/2)-3)/(-2*2) or x = (-25^(1/2)-3)/(-2*2)

x = -1/2 or x = 2

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

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

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

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

( x+1/2 )

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

x = -1/2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = -1/2

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