Question

How do you find vertical, horizontal and oblique asymptotes for `(x^2+4x-2)/(x-2)`?

Answer 1

Vertical: `uarr x = 2 darr`. Seldom realized oblique asymptote:
y = x+ 6. These are the asymptotes of the hyperbola represented by the equation. See illustrative graph.

Explanation:

Cross multiply and reorganize to the form

`x(y-x)-2y-4x+2=0`. This suggest the form

`(x+a)(y-x+b=c` and we have

`(x-2)(x-y+6)=-14` that represents the hyperbola with asymptotes

`x-2 = 0 and x-y+6=0`.

Now, look for the asymptotes in the graph.

graph{y(x-2)-x^2-4x+2=0 [-79.2, 79.2, -39.6, 39.6]}