How do you find the slant asymptote of f(x) =( x^2 + 3x – 3) / (x+4)?

Slant asymptote: ##y = x-1##. See the -inclusive graph.
By division
##y = f(x)= x-1+1/(x+4)##
Rearranged
##(y-x+1)(x+4)=1## revealing that the graph is a hyperbola with
asymptotes
##(y-x+1)(x+4)=0##.
Separately
y-x+1=0 gives a slant asymptote and
x+4=0 gives a vertical asymptote.
graph{((y-x+1)(x+4)-1)(y-x+1)(x+0.000001y+4)=0 [-23 23.02 -12.7 12.6]}