If x is positive then multiplying throughout by x gives

x^{2} - 3 < 2 x implying that (x - 3) (x + 1) < 0

This gives

0 < x < 3

If x is negative then multiplying throughout by x gives

x^{2} - 3 > 2 x implying that (x - 3) (x + 1) > 0

This has solutions

- 3 < x < - 1