x/x^2+2x-8=4/x-2-2/x+4

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


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

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

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

2*x^1-1*x^-1-10*x^0 = 0

(2*x^2-10*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^2-10*x^1-1*x^0) = 0

x^1

2*x^2-10*x-1 = 0

2*x^2-10*x-1 = 0

DELTA = (-10)^2-(-1*2*4)

DELTA = 108

DELTA > 0

x = (108^(1/2)+10)/(2*2) or x = (10-108^(1/2))/(2*2)

x = (6*3^(1/2)+10)/4 or x = (10-6*3^(1/2))/4

x in { (10-6*3^(1/2))/4, (6*3^(1/2)+10)/4} 

x in { (10-6*3^(1/2))/4, (6*3^(1/2)+10)/4 }

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