Oblique asymptotes of a rational function

[mindauggas]

Homework Statement

To find the oblique asymptotes of a rational function

(i) $f(x)=\frac{P(x)}{Q(x)}=\frac{a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{0}x^{0}}{b_{m}x^{m}+b_{m-1}x^{m-1}+...+b_{0}x^{0}}$

where $n=m+1$

we exprese it in a form

(ii) $f(x)=ax+b+\frac{R(x)}{Q(x)}$ using long division (my book says). The degree of R is less than the degree of Q.

Q.: How? Does one have to divide (i) and then add? How is the $f(x)=ax+b+\frac{R(x)}{Q(x)}$ obtained?

The Attempt at a Solution

 

[e^(i Pi)+1=0]

Those generalized expressions make my eyes bleed. You'll have a slant asymptote if the degree of the numerator is one higher than the denominator. To find out what it is, just divide the fraction and discard the remainder. This expression will be your slant asmptote.