Create an equation of a rational function for which the degree of the numerator is one more than the degree of the denominator, yet the function doesn’t have an OA.

Question

I don't get how can it not have an oblique assympotete

Answer 1

If the denominator is a factor of the numerator there is no OA.

For example: y=(x²-1)/(x-1), y=(x²+3x)/x. These functions have a “hole” but no OA.

IN GENERAL

For a quadratic numerator:

y=(ax²+bx-bc-ac²)/(x-c), where a, b and c are arbitrary constants and a≠0.