2x/(x-1)=5/(x-3)

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Solution for 2x/(x-1)=5/(x-3) equation: 


D( x )

x-3 = 0

x-1 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:3) U (3:+oo)

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

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

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

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

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

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

2*x^2-11*x+5 = 0

2*x^2-11*x+5 = 0

2*x^2-11*x+5 = 0

DELTA = (-11)^2-(2*4*5)

DELTA = 81

DELTA > 0

x = (81^(1/2)+11)/(2*2) or x = (11-81^(1/2))/(2*2)

x = 5 or x = 1/2

(x-1/2)*(x-5) = 0

((x-1/2)*(x-5))/((x-1)*(x-3)) = 0

((x-1/2)*(x-5))/((x-1)*(x-3)) = 0 // * (x-1)*(x-3)

(x-1/2)*(x-5) = 0

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 1/2, 5 }

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