Special Case

Example: f(x) = 3x^2 + x -2 / 2x^2 + 7x +5

First, factorize the function.
f(x) = (3x-2)(x+1)
         (2x+5)(x+1)

Simplify to a linear relationship
f(x) = (3x-2)
         (2x+5)
x cannot be -1 and -5/2.

Noticed that the graph has only one vertical asymptote, that is x=-5/2.
This is a special case because of a line that is discontinuous at x=-1.
This is the value at which the function is undefined.
Here, the discontinuity is not an asymptote but the point (-1, -5/3).
This type of discontinuity is called a hole or a gap.