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

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

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

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

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

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

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

x-3*x-2+6 = 0

4-2*x = 0

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

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

4-2*x = 0

4-2*x = 0 // - 4

-2*x = -4 // : -2

x = -4/(-2)

x = 2

x in { 2} 

x belongs to the empty set

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