What is the axis of symmetry in -7/x^2-4

I guess you probably mean

y = -7/ (x^2-4)

if x = 0 , y = -7/-4

if x = 1 , y = -7/-3
if x = -1, y = -7/-3

if x = 2, y = -7/0
if x = -2 y = -7/0

if x = 3, y = -7/5
if x = -3, y = -7/5

same left and right of x = 0 :)