(2/x)-(4/(x-2))=8/(x^2-2x)

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Solution for (2/x)-(4/(x-2))=8/(x^2-2x) equation: 


D( x )

x^2-(2*x) = 0

x-2 = 0

x = 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 = 0

x = 0

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

2/x-(4/(x-2)) = 8/(x^2-(2*x)) // - 8/(x^2-(2*x))

2/x-(4/(x-2))-(8/(x^2-(2*x))) = 0

2/x-4*(x-2)^-1-8*(x^2-2*x)^-1 = 0

2/x-4/(x-2)-8/(x^2-2*x) = 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-4/(x-2)-8/(x*(x-2)) = 0

(-4*x)/(x*(x-2))-8/(x*(x-2))+(2*(x-2))/(x*(x-2)) = 0

2*(x-2)-4*x-8 = 0

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

-2*x-12 = 0

(-2*x-12)/(x*(x-2)) = 0

(-2*x-12)/(x*(x-2)) = 0 // * x*(x-2)

-2*x-12 = 0

-2*x-12 = 0 // + 12

-2*x = 12 // : -2

x = 12/(-2)

x = -6

x = -6

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