Do some manipulation:

1/x > x (multiply both sides by 1/x)

1 > x^2 (take the square root of both sides)

+, - 1 = x

Check intervals:

- infinity to - 1

(-2)

1/-2 > -2 YES

-1 to 1

1/2 works, but -1/2 doesn't...hmmm

1/(1/2) > 1/2

2 > 1/2 YES

1/(-1/2) > -1/2

-2 > -1/2 NO

1 to infinity

(2)

1/2 > 2 NO

Solution

X < -1

0 < x < 1