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

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

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

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

x/(x-5)-5*(x-5)^-1-5 = 0

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

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

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

x-5*x-5+25 = 0

20-4*x = 0

(20-4*x)/(x-5) = 0

(20-4*x)/(x-5) = 0 // * x-5

20-4*x = 0

20-4*x = 0 // - 20

-4*x = -20 // : -4

x = -20/(-4)

x = 5

x in { 5} 

x belongs to the empty set

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