How to find the slant asymptote of the graph of the rational function

f(x)=x^2+x-20/x-6

Use synthetic division:

6 |.. 1 ... 1 ... -20
...|........ 6 .... 42
...-----------------------
.....1 .... 7 .... 22

→ The slant asymptote is y = x + 7

long division to get x^2+x-20 / x-6 = x + 7 + A/x-6 (the last term goes to 0 as x -> infinity)
so the slant asymptote is x + 7