Let me show you a way to solve this....
1 / [ x^2 - 1] >= 1/ [x - 1] and we can write
1/[x^2 - 1] - 1/[x - 1] >= 0 and getting a common denominator, we have
-x / [ x^2 - 1] > = 0
Note that this function does not exist at -1 or 1 because that would make the denominator 0
And note that when x = 0, the inequality is true
So the solutions come from one, or more, of these intervals :
(-infinity, -1), (-1, 0], [0, 1), (1, infinity)
Notice that if x < -1 the inequality is true
And if -1 < x < 0 the inequality is false
And if 0 <= x < 1 the inequality is true
And if x > 1, the inequality is false
Here's the graph : https://www.desmos.com/calculator/5qbwbakrao
