\[\boxed{\text{331.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\frac{1}{x^{3} - x^{2} + x - 1} + \frac{4x^{2} + 21}{x^{3} + x^{2} + x + 1} =\]
\[= \frac{4x^{3} - 3x^{2} + 14x - 4}{x^{4} - 1};\]
\[x^{4} - 1 =\]
\[= (x + 1)\left( x^{3} - x^{2} + x - 1 \right) =\]
\[= (x - 1)\left( x^{3} + x^{2} + x + 1 \right);\]
\[ОДЗ:\ \ \ x \neq \pm 1.\]
\[- x^{2} + 8x - 16 = 0\]
\[x^{2} - 8x + 16 = 0\]
\[(x - 4)^{2} = 0 \Longrightarrow x = 4.\]
\[Ответ:x = 4.\]