How do you find the slant asymptote of #y=((4x^3)+(x^2)+x+4)/((x^2)+5x)#?

1 Answer
Feb 20, 2016

Answer:

Slant asymptote is #y=(4x-19)#

Explanation:

While vertical asymptotes are given by solution of #(x^2+5x)=0# i.e. #x(x+5)=0# i.e. they are #x=0# and #x=-5#

To find slant asymptote of #y=(4x^3+x^2+x+4)/(x^2+5x)#, divide #(4x^3+x^2+x+4)# by #(x^2+5x)#, o

#4x(x^2+5x)-19(x^2+5x)+96x+4# i.e.

#y=(4x-19)+(96x+4)/(x^2+5x)#

Hence slant asymptote is #y=(4x-19)#