(5x)/(x-1)=(5/(x-1))+3

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Solution for (5x)/(x-1)=(5/(x-1))+3 equation: 


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:+oo)

(5*x)/(x-1) = 5/(x-1)+3 // - 5/(x-1)+3

(5*x)/(x-1)-(5/(x-1))-3 = 0

(5*x)/(x-1)-5*(x-1)^-1-3 = 0

(5*x)/(x-1)-5/(x-1)-3 = 0

(5*x)/(x-1)-5/(x-1)+(-3*(x-1))/(x-1) = 0

5*x-3*(x-1)-5 = 0

5*x-3*x-5+3 = 0

2*x-2 = 0

(2*x-2)/(x-1) = 0

(2*x-2)/(x-1) = 0 // * x-1

2*x-2 = 0

2*x-2 = 0 // + 2

2*x = 2 // : 2

x = 2/2

x = 1

x in { 1} 

x belongs to the empty set

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