Let $x be defined as x+(1/x) for all nonzero integers x. If $x=t, where t is an integer, which of the following is a possible value of t?

Let $x be defined as x+(1/x) for all nonzero integers x. If $x=t, where t is an integer, which of the following is a possible value of t? ($ is a symbol in this case)
a) 1
b) 0
c) -1
d) -2
e)-3

Is it d) because with all the other values (when you plug it in) factoring does not work out?
THANK YOU Mike!