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

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Solution for x+5/(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)

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

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

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

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

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

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

x^2-5*x-5*x+25 = 0

x^2-10*x+25 = 0

x^2-10*x+25 = 0

x^2-10*x+25 = 0

DELTA = (-10)^2-(1*4*25)

DELTA = 0

x = 10/(1*2)

x = 5 or x = 5

(x-5)^2 = 0

((x-5)^2)/(x-5) = 0

((x-5)^2)/(x-5) = 0 // * x-5

(x-5)^2 = 0

x-5 = 0 // + 5

x = 5

x in { 5} 

x belongs to the empty set

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