(11)/(x-8)=(x)/(3)

Solution for (11)/(x-8)=(x)/(3) equation:

D( x )

x-8 = 0

x-8 = 0

x-8 = 0

x-8 = 0 // + 8

x = 8

x in (-oo:8) U (8:+oo)

11/(x-8) = x/3 // - x/3

11/(x-8)-(x/3) = 0

11/(x-8)-x/3 = 0

(3*11)/(3*(x-8))+(-x*(x-8))/(3*(x-8)) = 0

3*11-x*(x-8) = 0

8*x-x^2+33 = 0

8*x-x^2+33 = 0

8*x-x^2+33 = 0

DELTA = 8^2-(-1*4*33)

DELTA = 196

DELTA > 0

x = (196^(1/2)-8)/(-1*2) or x = (-196^(1/2)-8)/(-1*2)

x = -3 or x = 11

(x+3)*(x-11) = 0

((x+3)*(x-11))/(3*(x-8)) = 0

((x+3)*(x-11))/(3*(x-8)) = 0 // * 3*(x-8)

(x+3)*(x-11) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-11 )

x-11 = 0 // + 11

x = 11

x in { -3, 11 }