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

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

D( x )

x = 0

x+3 = 0

x = 0

x = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:0) U (0:+oo)

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

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

(x-3)/x-8*(x+3)^-1 = 0

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

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

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

x^2-8*x-9 = 0

x^2-8*x-9 = 0

x^2-8*x-9 = 0

DELTA = (-8)^2-(-9*1*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)+8)/(1*2) or x = (8-100^(1/2))/(1*2)

x = 9 or x = -1

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

((x+1)*(x-9))/(x*(x+3)) = 0

((x+1)*(x-9))/(x*(x+3)) = 0 // * x*(x+3)

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x-9 )

x-9 = 0 // + 9

x = 9

x in { -1, 9 }