Find the vertical asymptotes of the rational function hxx2x2

Find the vertical asymptotes of the rational function. h(x)=x+2/x^2-36

Solution

We have the function h(x) = (x+2)/(x²-36)

h(x) = (x+2)/((x+6)(x-6))

Vertical asymptotes occur when denominator is zero.

That is, (x-6)(x+6) = 0

x-6 = 0 gives x = 6

x+6=0 gives x = -6

Therefore, the required vertical asymptotes are x = -6 and x = 6