(8/(x^2-2x))-(9/x)=(3/(x-2))

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Solution for (8/(x^2-2x))-(9/x)=(3/(x-2)) 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)

8/(x^2-(2*x))-(9/x) = 3/(x-2) // - 3/(x-2)

8/(x^2-(2*x))-(3/(x-2))-(9/x) = 0

8/(x^2-2*x)-3*(x-2)^-1-9*x^-1 = 0

8/(x^2-2*x)-3/(x-2)-9/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

8/(x*(x-2))-3/(x-2)-9/x = 0

8/(x*(x-2))+(-3*x)/(x*(x-2))+(-9*(x-2))/(x*(x-2)) = 0

8-9*(x-2)-3*x = 0

8-3*x-9*x+18 = 0

26-12*x = 0

(26-12*x)/(x*(x-2)) = 0

(26-12*x)/(x*(x-2)) = 0 // * x*(x-2)

26-12*x = 0

26-12*x = 0 // - 26

-12*x = -26 // : -12

x = -26/(-12)

x = 13/6

x = 13/6

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