To solve this equation, we first need to simplify the expression:

(X^2-9)/(X^3+2X^2+9) = ((X-3)(X+3))/(X(X^2+2X+9))

Now we can set the expression equal to zero:

((X-3)(X+3))/(X(X^2+2X+9)) = 0

This expression will be equal to zero if the numerator, (X-3)(X+3), is equal to zero. So we set each factor equal to zero:

X-3 = 0 or X+3 = 0

X = 3 or X = -3

Therefore, the solutions to the equation are X = 3 and X = -3.