I don't know whether to post this in an Algebra section or a Calculus section so I just chose Algebra. I have a small understanding of limits if it is possible to solve the following equation in that manner. To the point, the following equation should have a horizontal asymptote at 1 and a vertical asymptote at -2 and 1, all of these are true except at the point (-3.5, 1) exists and there is no possibility of it being a hole because there is no canceling factor in the numerator and the denominator for two reasons:

1) The numerator cannot be factored

2) Both of the factors of the denominator are vertical asymptotes

If someone could attempt to rationalize this for me I would be very much appreciative. I love math and spend countless hours working with it, for fun. I was studying Pre-Calculus in my free time in my Algebra 2 w/ Trig. class, I had a lot of free time due to my extensive understanding of mathematics.

Here is the original equation I am referring to:

(x^2 + 3x + 1)/(x^2 + x - 2)