x=6/(x-1)

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Solution for x=6/(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 = 6/(x-1) // - 6/(x-1)

x-(6/(x-1)) = 0

x-6*(x-1)^-1 = 0

x-6/(x-1) = 0

(x*(x-1))/(x-1)-6/(x-1) = 0

x*(x-1)-6 = 0

x^2-x-6 = 0

x^2-x-6 = 0

x^2-x-6 = 0

DELTA = (-1)^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+1)/(1*2) or x = (1-25^(1/2))/(1*2)

x = 3 or x = -2

(x+2)*(x-3) = 0

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

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

(x+2)*(x-3) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { -2, 3 }

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