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

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


D( x )

x-5 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x in (-oo:5) U (5:+oo)

(3*x)/(x-5) = y // - y

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

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

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

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

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

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

x*(-y) = -(5*y) // : -y

x = (-(5*y))/(-y)

x = 5

x-5 = 0

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

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

x-5 = 0

x-5 = 0 // + 5

x = 5

x in { 5} 

x belongs to the empty set

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