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

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

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

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

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

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

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

x-3 = 0

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

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

x-3 = 0

x-3 = 0 // + 3

x = 3

x in { 3} 

x belongs to the empty set

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