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

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Solution for x/(x-1)=1/(x-1)-1/(x-3) equation: 


D( x )

x-3 = 0

x-1 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:3) U (3:+oo)

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

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

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

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

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

x*(x-3)-1*(x-3)+1*(x-1) = 0

x^2-4*x+x-1+3 = 0

x^2-3*x+2 = 0

x^2-3*x+2 = 0

x^2-3*x+2 = 0

DELTA = (-3)^2-(1*2*4)

DELTA = 1

DELTA > 0

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

x = 2 or x = 1

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

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

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

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

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 1} 

x = 2

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