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

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

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

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

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

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

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

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

x+5*x-15-3 = 0

6*x-18 = 0

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

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

6*x-18 = 0

6*x-18 = 0 // + 18

6*x = 18 // : 6

x = 18/6

x = 3

x in { 3} 

x belongs to the empty set

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