2x/(x-3)+3=6/(x-3)

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Solution for 2x/(x-3)+3=6/(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)

(2*x)/(x-3)+3 = 6/(x-3) // - 6/(x-3)

(2*x)/(x-3)-(6/(x-3))+3 = 0

(2*x)/(x-3)-6*(x-3)^-1+3 = 0

(2*x)/(x-3)-6/(x-3)+3 = 0

(2*x)/(x-3)-6/(x-3)+(3*(x-3))/(x-3) = 0

3*(x-3)+2*x-6 = 0

2*x+3*x-9-6 = 0

5*x-15 = 0

(5*x-15)/(x-3) = 0

(5*x-15)/(x-3) = 0 // * x-3

5*x-15 = 0

5*x-15 = 0 // + 15

5*x = 15 // : 5

x = 15/5

x = 3

x in { 3} 

x belongs to the empty set

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