y=x/(x-5)

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Solution for y=x/(x-5) 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)

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

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

(-1*x)/(x-5)+y = 0

(-1*x)/(x-5)+(y*(x-5))/(x-5) = 0

y*(x-5)-1*x = 0

x*y-x-5*y = 0

x*y-x-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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