Question 887756
The graph of y= x^2-7x+12/x^2-1 is this:


{{{graph(300,300,-25,25,-15,40,x^2-7x+12/x^2-1)}}}


But that is not what you want.


You want this:
y= (x^2-7x+12)/(x^2-1)
{{{y= (x^2-7x+12)/(x^2-1)}}}
-
That seems not factorable to simplify, but there is still some information to learn about the graph if factor the function.
{{{y=((x-3)(x-4))/((x-1)(x+1))}}}
Zeros at x=3 and x=4.
Asymtptotes (vertical) at x=1 and x=-1.
You can test the intervals around all critical points...


THIS is the graph. (Difficult for this to appear well on the system)
{{{graph(400,400,-15,15,-15,15,(x^2-7x+12)/(x^2-1))}}}


A zoom-in on the right side
{{{graph(300,300,2,5,-1,1,(x^2-7x+12)/(x^2-1))}}}