((11x-33)/(x-4))+(5/x)=(-5/(x^2-4x))

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Solution for ((11x-33)/(x-4))+(5/x)=(-5/(x^2-4x)) equation: 


D( x )

x = 0

x^2-(4*x) = 0

x-4 = 0

x = 0

x = 0

x^2-(4*x) = 0

x^2-(4*x) = 0

x^2-4*x = 0

x^2-4*x = 0

DELTA = (-4)^2-(0*1*4)

DELTA = 16

DELTA > 0

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

x = 4 or x = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:0) U (0:4) U (4:+oo)

(11*x-33)/(x-4)+5/x = -5/(x^2-(4*x)) // + -5/(x^2-(4*x))

(11*x-33)/(x-4)-(-5/(x^2-(4*x)))+5/x = 0

(11*x-33)/(x-4)+5*(x^2-4*x)^-1+5/x = 0

(11*x-33)/(x-4)+5/(x^2-4*x)+5/x = 0

x^2-4*x = 0

x^2-4*x = 0

x*(x-4) = 0

x-4 = 0 // + 4

x = 4

x*(x-4) = 0

(11*x-33)/(x-4)+5/(x*(x-4))+5/x = 0

(x*(11*x-33))/(x*(x-4))+5/(x*(x-4))+(5*(x-4))/(x*(x-4)) = 0

x*(11*x-33)+5*(x-4)+5 = 0

11*x^2-33*x+5*x-20+5 = 0

11*x^2-28*x-15 = 0

11*x^2-28*x-15 = 0

11*x^2-28*x-15 = 0

DELTA = (-28)^2-(-15*4*11)

DELTA = 1444

DELTA > 0

x = (1444^(1/2)+28)/(2*11) or x = (28-1444^(1/2))/(2*11)

x = 3 or x = -5/11

(x+5/11)*(x-3) = 0

((x+5/11)*(x-3))/(x*(x-4)) = 0

((x+5/11)*(x-3))/(x*(x-4)) = 0 // * x*(x-4)

(x+5/11)*(x-3) = 0

( x+5/11 )

x+5/11 = 0 // - 5/11

x = -5/11

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -5/11, 3 }

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