Answer
odd
Work Step by Step
We know that if a function is odd, then $f(-x)=-f(x).$
We know that if a function is even, then $f(-x)=f(x).$
Hence we plug in $-x$ to see what happens.
$f(-x)=\frac{-(-x)}{(-x)^2+9}=\frac{x}{x^2+9}=-f(x).$ Therefore the function is odd.