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

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


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

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

x-(x/(x-2))+4/4 = 0

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

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

x*(x-2)+1*(x-2)-1*x = 0

x^2-3*x+x-2 = 0

x^2-2*x-2 = 0

x^2-2*x-2 = 0

x^2-2*x-2 = 0

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

DELTA = 12

DELTA > 0

x = (12^(1/2)+2)/(1*2) or x = (2-12^(1/2))/(1*2)

x = (2*3^(1/2)+2)/2 or x = (2-2*3^(1/2))/2

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

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

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

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

( x-((2*3^(1/2)+2)/2) )

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

x = (2*3^(1/2)+2)/2

( x-((2-2*3^(1/2))/2) )

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

x = (2-2*3^(1/2))/2

x in { (2*3^(1/2)+2)/2, (2-2*3^(1/2))/2 }

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