(1/(x-2))-(2/(x^2-2x))=4

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Solution for (1/(x-2))-(2/(x^2-2x))=4 equation: 


D( x )

x^2-(2*x) = 0

x-2 = 0

x^2-(2*x) = 0

x^2-(2*x) = 0

x^2-2*x = 0

x^2-2*x = 0

DELTA = (-2)^2-(0*1*4)

DELTA = 4

DELTA > 0

x = (4^(1/2)+2)/(1*2) or x = (2-4^(1/2))/(1*2)

x = 2 or x = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:0) U (0:2) U (2:+oo)

1/(x-2)-(2/(x^2-(2*x))) = 4 // - 4

1/(x-2)-(2/(x^2-(2*x)))-4 = 0

1/(x-2)-2*(x^2-2*x)^-1-4 = 0

1/(x-2)-2/(x^2-2*x)-4 = 0

x^2-2*x = 0

x^2-2*x = 0

x*(x-2) = 0

x-2 = 0 // + 2

x = 2

x*(x-2) = 0

1/(x-2)-2/(x*(x-2))-4 = 0

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

1*x-4*x*(x-2)-2 = 0

x-4*x^2+8*x-2 = 0

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

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

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

DELTA = 9^2-(-4*(-2)*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-9)/(-4*2) or x = (-49^(1/2)-9)/(-4*2)

x = 1/4 or x = 2

(x-1/4)*(x-2) = 0

((x-1/4)*(x-2))/(x*(x-2)) = 0

((x-1/4)*(x-2))/(x*(x-2)) = 0 // * x*(x-2)

(x-1/4)*(x-2) = 0

( x-1/4 )

x-1/4 = 0 // + 1/4

x = 1/4

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = 1/4

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