3/x+5+2/2x+1=4/x-2

Solution for 3/x+5+2/2x+1=4/x-2 equation:

D( x )

x = 0

x = 0

x = 0

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

(2/2)*x+3/x+1+5 = 4/x-2 // - 4/x-2

(2/2)*x+3/x-(4/x)+1+2+5 = 0

(2/2)*x+3/x-4*x^-1+1+2+5 = 0

1*x^1-1*x^-1+8*x^0 = 0

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

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

x^1

x^2+8*x-1 = 0

x^2+8*x-1 = 0

DELTA = 8^2-(-1*1*4)

DELTA = 68

DELTA > 0

x = (68^(1/2)-8)/(1*2) or x = (-68^(1/2)-8)/(1*2)

x = (2*17^(1/2)-8)/2 or x = (-2*17^(1/2)-8)/2

x in { (-2*17^(1/2)-8)/2, (2*17^(1/2)-8)/2} 

x in { (-2*17^(1/2)-8)/2, (2*17^(1/2)-8)/2 }