\(\left( {{x^2} + x-2} \right)\left( {x-4} \right) > 0.\)
Решим неравенство методом интервалов:
\(\left( {{x^2} + x-2} \right)\left( {x-4} \right) = 0\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{{x^2} + x-2 = 0,}\\{x-4 = 0\,\,\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left[ {\begin{array}{*{20}{c}}{x = 1,\,\,\,\,}\\{x = -2,}\\{x = 4.\,\,}\end{array}} \right.\)
Следовательно, решение исходного неравенства: \(x\, \in \,\left( {-2;1} \right) \cup \left( {4; + \infty } \right).\)
Ответ: \(\left( {-2;\;1} \right) \cup \left( {4;\; + \infty } \right).\)