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

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

It’s D because the only way you get an integer out of x+\dfrac{1}{x} is if x = 1 or x = –1. When x = –1, -1+\dfrac{1}{-1}=-2. (When x = 1, 1+\dfrac{1}{1}=2, but 2 isn’t an answer choice.)

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