What values of x must be excluded from the domain of f(x) = (x+5)/(x²-9)?

A rational function is undefined where its denominator is zero. Set $x^2-9=0$, so $(x-3)(x+3)=0$ and $x=3$ or $x=-3$. Both values must be excluded, choice H. The numerator plays no role in the excluded values here, because it does not cancel with any factor of the denominator. Choice F ($5$) confuses the problem with the numerator, which is zero at $x=-5$, and a zero in the numerator is perfectly allowed. Choice G ($3$ only) misses $x=-3$, since $(-3)^2=9$ also. Choice J ($9$) confuses $x^2=9$ with $x=9$. Check: $(-3)^2-9=0$.