Question

Solve: 1/x + 1/(x-1) < 0

Answer 1

1/x + 1/(x-1) < 0

(x - 1 + x)/x(x-1)<0
2x - 1 < 0 , x does not equal to 0 and 1.
x<1/2.
Thus the answer is (-inf, 0) and (0, 1/2)