(18)/(x)=(x+9)/(x-1)

Solution for (18)/(x)=(x+9)/(x-1) equation:

D( x )

x = 0

x-1 = 0

x = 0

x = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:0) U (0:1) U (1:+oo)

18/x = (x+9)/(x-1) // - (x+9)/(x-1)

18/x-((x+9)/(x-1)) = 0

(-1*(x+9))/(x-1)+18/x = 0

(-1*x*(x+9))/(x*(x-1))+(18*(x-1))/(x*(x-1)) = 0

18*(x-1)-1*x*(x+9) = 0

9*x-x^2-18 = 0

9*x-x^2-18 = 0

9*x-x^2-18 = 0

DELTA = 9^2-(-18*(-1)*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-9)/(-1*2) or x = (-9^(1/2)-9)/(-1*2)

x = 3 or x = 6

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

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

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

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

( x-3 )

x-3 = 0 // + 3

x = 3

( x-6 )

x-6 = 0 // + 6

x = 6

x in { 3, 6 }