((3x+1)/(x-2))+(4/x)=(-8/(x^2-2x))

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Solution for ((3x+1)/(x-2))+(4/x)=(-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)

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

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

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

(3*x+1)/(x-2)+8/(x^2-2*x)+4/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

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

(x*(3*x+1))/(x*(x-2))+8/(x*(x-2))+(4*(x-2))/(x*(x-2)) = 0

x*(3*x+1)+4*(x-2)+8 = 0

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

3*x^2+5*x = 0

3*x^2+5*x = 0

x*(3*x+5) = 0

3*x+5 = 0 // - 5

3*x = -5 // : 3

x = -5/3

x*(x+5/3) = 0

(x*(x+5/3))/(x*(x-2)) = 0

(x*(x+5/3))/(x*(x-2)) = 0 // * x*(x-2)

x*(x+5/3) = 0

( x+5/3 )

x+5/3 = 0 // - 5/3

x = -5/3

( x )

x = 0

x in { 0} 

x = -5/3

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