To solve this inequality, we first need to isolate the variable x.

3/x - 1 >= x + 1

Add 1 to both sides:

3/x >= x + 2

Multiply both sides by x to get rid of the fraction:

3 >= x^2 + 2x

Rearrange to set the inequality to zero:

x^2 + 2x - 3 <= 0

Now we need to factorize the quadratic equation:

(x + 3)(x - 1) <= 0

This gives us the solutions x <= -3 and x >= 1.

So, the solution to the original inequality is x <= -3 or x >= 1.