(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)-4-2 // - 4/x-(2/x)-4-2

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

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

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

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

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

x^1

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

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

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

DELTA = 12

DELTA > 0

x = (12^(1/2)+2)/(2*2) or x = (2-12^(1/2))/(2*2)

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

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

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

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