\[y = \frac{x^{4} - 1}{x}\]
\[y( - x) = \frac{( - x)^{4} - 1}{- x} = \frac{x^{4} - 1}{- x}\]
\[Так\ как\ y( - x) = - y(x);\ \ то\]
\[\text{\ \ f}(x) - нечетная.\]