Let $f(x)=\frac{-x^2+x+2}{x^2-5x+6}.$ What is the equation of the vertical asymptote of $f(x)$ and what is the sign of $f(x)$ as $x$ approaches the asymptote from the right?

$x=2,$ positive

$x=2,$ negative

$x=3,$ positive

$x=3,$ negative