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

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Solution for (2/(x-2))-(4/(x^2-2x))=2 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)

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

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

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

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

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

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

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

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

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

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

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

3*x-x^2-2 = 0

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

DELTA = 1

DELTA > 0

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

x = 1 or x = 2

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

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

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

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

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2} 

x = 1

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