2/(x-3)=(x-2)/6

Solution for 2/(x-3)=(x-2)/6 equation:

D( x )

x-3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

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

2/(x-3) = (x-2)/6 // - (x-2)/6

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

2/(x-3)+(-1*(x-2))/6 = 0

(2*6)/(6*(x-3))+(-1*(x-2)*(x-3))/(6*(x-3)) = 0

2*6-1*(x-2)*(x-3) = 0

5*x-x^2+6 = 0

5*x-x^2+6 = 0

5*x-x^2+6 = 0

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

DELTA = 49

DELTA > 0

x = (49^(1/2)-5)/(-1*2) or x = (-49^(1/2)-5)/(-1*2)

x = -1 or x = 6

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

((x+1)*(x-6))/(6*(x-3)) = 0

((x+1)*(x-6))/(6*(x-3)) = 0 // * 6*(x-3)

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -1, 6 }