3/x+3=5/2x+6+2/x-2

Solution for 3/x+3=5/2x+6+2/x-2 equation:

D( x )

x = 0

x = 0

x = 0

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

3/x+3 = (5/2)*x+2/x-2+6 // - (5/2)*x+2/x-2+6

3/x-((5/2)*x)-(2/x)-6+2+3 = 0

(-5/2)*x+3/x-2*x^-1-6+2+3 = 0

1*x^-1-5/2*x^1-1*x^0 = 0

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

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

x^1

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

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

DELTA = (-1)^2-(1*4*(-5/2))

DELTA = 11

DELTA > 0

x = (11^(1/2)+1)/(2*(-5/2)) or x = (1-11^(1/2))/(2*(-5/2))

x = (11^(1/2)+1)/(-5) or x = (1-11^(1/2))/(-5)

x in { (11^(1/2)+1)/(-5), (1-11^(1/2))/(-5)} 

x in { (11^(1/2)+1)/(-5), (1-11^(1/2))/(-5) }