x-4/x-3=9/x-3-1/4

Solution for x-4/x-3=9/x-3-1/4 equation:

D( x )

x = 0

x = 0

x = 0

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

x-(4/x)-3 = 9/x-(1/4)-3 // - 9/x-(1/4)-3

x-(4/x)-(9/x)+1/4-3+3 = 0

x-4*x^-1-9*x^-1+1/4-3+3 = 0

1*x^1-13*x^-1+1/4*x^0 = 0

(1*x^2+1/4*x^1-13*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2+1/4*x^1-13*x^0) = 0

x^1

x^2+(1/4)*x-13 = 0

x^2+(1/4)*x-13 = 0

DELTA = (1/4)^2-(-13*1*4)

DELTA = 833/16

DELTA > 0

x = ((833/16)^(1/2)-(1/4))/(1*2) or x = (-(1/4)-(833/16)^(1/2))/(1*2)

x = ((833/16)^(1/2)-1/4)/2 or x = (-((833/16)^(1/2)+1/4))/2

x in { (-((833/16)^(1/2)+1/4))/2, ((833/16)^(1/2)-1/4)/2} 

x in { (-((833/16)^(1/2)+1/4))/2, ((833/16)^(1/2)-1/4)/2 }