(x/(x-2))=(2/(x-2))-(2/3)

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Solution for (x/(x-2))=(2/(x-2))-(2/3) 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/(x-2) = 2/(x-2)-(2/3) // - 2/(x-2)-(2/3)

x/(x-2)-(2/(x-2))+2/3 = 0

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

x/(x-2)-2/(x-2)+2/3 = 0

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

2*(x-2)+3*x-2*3 = 0

3*x+2*x-6-4 = 0

5*x-10 = 0

(5*x-10)/(3*(x-2)) = 0

(5*x-10)/(3*(x-2)) = 0 // * 3*(x-2)

5*x-10 = 0

5*x-10 = 0 // + 10

5*x = 10 // : 5

x = 10/5

x = 2

x in { 2} 

x belongs to the empty set

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