Question 1038673
{{{ f(x)=(x^2+x-6)/(x^2-5x+6) = ((x+3 ) (x-2))/((x-3)(x-2)) = (x+3)/(x-3) = 1+6/(x-3)}}}

There is a removable discontinuity at x = 2 (a "hole"), while there is an infinite discontinuity at x = 3.  The graph of f(x) is obtained from y = 1/x by horizontal translation of 3 units to the right, followed by a vertical stretching by a factor of 6, and then a vertical translation by 1 unit, and finally "puncturing" the resulting graph at the point (2,-5).