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

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

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

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

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

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

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

x^2-5*x-14 = 0

x^2-5*x-14 = 0

x^2-5*x-14 = 0

DELTA = (-5)^2-(-14*1*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)+5)/(1*2) or x = (5-81^(1/2))/(1*2)

x = 7 or x = -2

(x+2)*(x-7) = 0

((x+2)*(x-7))/(3*(x-1)) = 0

((x+2)*(x-7))/(3*(x-1)) = 0 // * 3*(x-1)

(x+2)*(x-7) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-7 )

x-7 = 0 // + 7

x = 7

x in { -2, 7 }