Is f(x)= -x/x^2-1 odd, even or neither of the two functions?

Answer 1

if even: f(-x) = f(x)
if odd : f(-x) = -f(x)

check for a given value:
e.g. x = 5
f(-5) = 5/24
f(5) = -5/24 ---- > not even

f(5) = -5/24
f(-5) = 5/24 = -f(5)

should be obvious that the function is odd
since
f(-x) = -(-x)/(x^2-1)
= x/(x^2-1)
= - f(x)