\[\frac{x^{5} + 1}{x^{8} + x^{3}} = \frac{x^{5} + 1}{x^{3}(x^{5} + 1)} = \frac{1}{x^{3}}\ \]
\[x = 0,1:\]
\[\frac{1}{x^{3}} = \frac{1}{0,001} = 1000.\]
\[x = - \frac{1}{3}:\ \ \ \ \]
\[\frac{1}{x^{3}} = \frac{1}{- \frac{1}{27}} = - 27.\]