Finding Oblique Asympote by polidiv

That depends on the definition of asymptote - do you call a function "asymptote" if it is identical to the function you consider?
As in, is g(x)=x+1 an asymptote to f(x)=x+1?

 

I'm having a hard time understanding what you're asking.

"where the x^n+1/x^n or any" - what does this mean?
Also, the expression you wrote probably isn't what you meant. What you wrote is this:
xⁿ + 1/xⁿ

I can't tell if you meant ##\frac{x^{n + 1}}{x^n}## or ##\frac{x^n + 1}{x^n}##. Suitably placed parentheses would be a great help.

"perfect match wihout any Rests" - ??