Question

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

Answer 1

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)`