Answer
$\{x| x\lt-4\ or\ x\gt1 \}$.
Work Step by Step
$\frac{x-1}{x+4}\gt0$ gives boundary points $x=-4,1$, the "$\gt$" sign implies that the solutions are "outside" the region formed by the 2 boundary points, thus we have $\{x| x\lt-4\ or\ x\gt1 \}$.
