((x)/(x-6))=((1)/(x-4))

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Solution for ((x)/(x-6))=((1)/(x-4)) equation: 


D( x )

x-6 = 0

x-4 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:4) U (4:6) U (6:+oo)

x/(x-6) = 1/(x-4) // - 1/(x-4)

x/(x-6)-(1/(x-4)) = 0

x/(x-6)-(x-4)^-1 = 0

x/(x-6)-1/(x-4) = 0

(x*(x-4))/((x-6)*(x-4))+(-1*(x-6))/((x-6)*(x-4)) = 0

x*(x-4)-1*(x-6) = 0

x^2-5*x+6 = 0

x^2-5*x+6 = 0

x^2-5*x+6 = 0

DELTA = (-5)^2-(1*4*6)

DELTA = 1

DELTA > 0

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

x = 3 or x = 2

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

((x-2)*(x-3))/((x-6)*(x-4)) = 0

((x-2)*(x-3))/((x-6)*(x-4)) = 0 // * (x-6)*(x-4)

(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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