(x-1)/(x-5)=4/(x-5)

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Solution for (x-1)/(x-5)=4/(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-1)/(x-5) = 4/(x-5) // - 4/(x-5)

(x-1)/(x-5)-(4/(x-5)) = 0

(x-1)/(x-5)-4*(x-5)^-1 = 0

(x-1)/(x-5)-4/(x-5) = 0

x-4-1 = 0

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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