1/(x-4)=1+4/(x^2-4x)

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Solution for 1/(x-4)=1+4/(x^2-4x) equation: 


D( x )

x^2-(4*x) = 0

x-4 = 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)

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

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

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

1/(x-4)-4/(x^2-4*x)-1 = 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

1/(x-4)-4/(x*(x-4))-1 = 0

(1*x)/(x*(x-4))-4/(x*(x-4))+(-1*x*(x-4))/(x*(x-4)) = 0

1*x-1*x*(x-4)-4 = 0

x-x^2+4*x-4 = 0

5*x-x^2-4 = 0

5*x-x^2-4 = 0

5*x-x^2-4 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)-5)/(-1*2) or x = (-9^(1/2)-5)/(-1*2)

x = 1 or x = 4

(x-1)*(x-4) = 0

((x-1)*(x-4))/(x*(x-4)) = 0

((x-1)*(x-4))/(x*(x-4)) = 0 // * x*(x-4)

(x-1)*(x-4) = 0

( x-1 )

x-1 = 0 // + 1

x = 1

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 4} 

x = 1

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