For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x minus five divided by the quantity x squared minus one

Step-by-step explanation:

The function is:

             x - 5

f(x) =

            x^2 - 1

Horizontal asymptote:  observe that as x grows towards infinity, the function (and graph) approaches y = 0.  This is the horizontal asymptote.

Vertical asymptote:  These occur whenever the denominator of a rational function becomes zero.  Here the vertical asymptotes are  x = ± 1.

so, converting firstly the mixed fractions to improper fractions and then "adding".