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

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

D( x )

x = 0

x = 0

x = 0

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

x+x-(1/x)-(x/x)-1 = 5/2 // - 5/2

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

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

2*x^1-1*x^-1-9/2*x^0 = 0

(2*x^2-9/2*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^2-9/2*x^1-1*x^0) = 0

x^1

2*x^2+(-9/2)*x-1 = 0

2*x^2+(-9/2)*x-1 = 0

DELTA = (-9/2)^2-(-1*2*4)

DELTA = 113/4

DELTA > 0

x = ((113/4)^(1/2)-(-9/2))/(2*2) or x = (-(-9/2)-(113/4)^(1/2))/(2*2)

x = ((113/4)^(1/2)+9/2)/4 or x = (9/2-(113/4)^(1/2))/4

x in { (9/2-(113/4)^(1/2))/4, ((113/4)^(1/2)+9/2)/4} 

x in { (9/2-(113/4)^(1/2))/4, ((113/4)^(1/2)+9/2)/4 }