4/x - x/4 < 8/x - 3·x/4
(16 - x^2)/(4·x) < (32 - 3·x^2)/(4·x)
Fall1: x > 0
16 - x^2 < 32 - 3·x^2
2·x^2 - 16 < 0 --> - 2·√2 < x < 2·√2 --> 0 < x < 2·√2
Fall2: x < 0
16 - x^2 > 32 - 3·x^2
2·x^2 - 16 > 0 --> x < - 2·√2 ∨ x > 2·√2 --> x < - 2·√2
Lösung ist demnach
x < - 2·√2 ∨ 0 < x < 2·√2