Answer
$(x\lt-2)∪(1\lt x\lt2)$
Work Step by Step
Following the solving steps of inequality, we write:
$\frac{5}{x^3-x^2-4x+4}\lt0$
Let the expression on the left side of inequality equal to $y$
$y=\frac{5}{x^3-x^2-4x+4}$ and graph it.
See the red graph on the image above. We need the part of the graph that lies below $x$-axis as we are asked for ($\lt$) in the beginning.
So our solution is $(−\infty,-2) ∪ (1, 2)$
Using interval notation: $(x\lt-2)∪(1\lt x\lt2)$
