We have the following information about a function $f(x)$ :

The function has a removable discontinuity at $x=2.$

The function has an infinite discontinuity at $x=3.$

The horizontal asymptote for this function is $y=0.$ Which of the following can be the formula for $f(x)?$

$f(x)=\frac{x^2-2x}{x^2-5x6}$

$f(x)=\frac{5x-10}{x^{2}5x6}$

$f(x)=\frac{5x^2-10x}{x^2-5x6}$

$f(x)=\frac{5x-10}{x^2-5x6}$

$f(x)=\frac{5x-10}{x^2-9}$

None of the above.