(4x)/(x-9)=y

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Solution for (4x)/(x-9)=y equation: 


D( x )

x-9 = 0

x-9 = 0

x-9 = 0

x-9 = 0 // + 9

x = 9

x in (-oo:9) U (9:+oo)

(4*x)/(x-9) = y // - y

(4*x)/(x-9)-y = 0

(4*x)/(x-9)+(-y*(x-9))/(x-9) = 0

4*x-y*(x-9) = 0

4*x-(x*y)+9*y = 0

4*x-(x*y)+9*y = 0

x*(-y)+9*y = 0 // - 9*y

x*(-y) = -(9*y) // : -y

x = (-(9*y))/(-y)

x = 9

x-9 = 0

(x-9)/(x-9) = 0

(x-9)/(x-9) = 0 // * x-9

x-9 = 0

x-9 = 0 // + 9

x = 9

x in { 9} 

x belongs to the empty set

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