Answer
$(-∞, -1) U [1, ∞)$
Work Step by Step
$\frac{x-1}{x^3 + 1} \geq 0$
$\frac{x-1}{(x+1)(x^2 - x + 1)} \geq 0$
Find the zeros of the expressions in the numerator AND the denominator
$x = 1, -1$
Test numbers in between those zero values to determine if the function is negative or positive
$(-∞, -1)$ $\frac{(-)}{(-)(+)} = (+)$
$(-1, 1]$ $\frac{(-)}{(+)(+)} = (-)$
$[1, ∞)$ $\frac{(+)}{(+)(+)} = (+)$
Thus the solution is $(-∞, -1) U [1, ∞)$
