3/(x-3)=5+x/(x-3)

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Solution for 3/(x-3)=5+x/(x-3) equation: 


D( x )

x-3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

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

3/(x-3) = x/(x-3)+5 // - x/(x-3)+5

3/(x-3)-(x/(x-3))-5 = 0

3/(x-3)+(-1*x)/(x-3)-5 = 0

3/(x-3)+(-1*x)/(x-3)+(-5*(x-3))/(x-3) = 0

3-5*(x-3)-1*x = 0

3-x-5*x+15 = 0

18-6*x = 0

(18-6*x)/(x-3) = 0

(18-6*x)/(x-3) = 0 // * x-3

18-6*x = 0

18-6*x = 0 // - 18

-6*x = -18 // : -6

x = -18/(-6)

x = 3

x in { 3} 

x belongs to the empty set

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