First, we need to find the domain of the function.
We can not divide by zero, therefore:
[tex]9x^2-4\neq0\ \ \ \ |\text{add 4 to both sides}\\\\9x^2\neq4\ \ \ \ |\text{divide both sides by 9}\\\\x^2\neq\dfrac{4}{9}\ \ \ \ \ |\text{square root both sides}\\\\x\neq\pm\sqrt{\dfrac{4}{9}}\\\\x\neq-\dfrac{2}{3}\ \wedge\ x\neq\dfrac{2}{3}[/tex]
The zeros of function are x-s, for which f(x) = 0:
[tex]f(x)=\dfrac{x}{9x^2-4}\\\\f(x)=0\Rightarrow\dfrac{x}{9x^2-4}=0[/tex]
The fraction is zero if the numerator is equal to zero. Therefore:
[tex]f(x)=0\iff x=0\in D[/tex]
