Answer
$(-\infty,-2)U(0,1)$
Work Step by Step
Step 1. Graph $R(x)=\frac{x}{(x-1)(x+2)}$ as shown in the figure.
Step 2. The vertical asymptotes ($x=-2,1$) and a zero ($x=0$) divide the x-axis into four intervals $(-\infty,-2),(-2,0),(0,1),(1,\infty)$
Step 3. For $R(x)\lt0$, we can identify the solution intervals as $(-\infty,-2)U(0,1)$