How to solve $\frac{x+2}{3-x} \le 0$ I know that $a/b<0$ if both $a$ and $b$ is $<0$ or both $a$ and $b >0$. However when I did that $a$ in this case $(x+2)$ was less than or equal to $0$ but $b$ or $(3-x)$ was not less than or equal to $0$. 

As an alternate approach note that $\frac{a}{b}$ will have exactly the same sign as $ab$ so you can sketch (or visualize in your head) the graph of $(x+2)(3-x)$ and consider when it is zero or less.
Note you need to treat the case of $ab=0$ carefully as it doesn't have the same solutions as $\frac{a}{b}=0$ because you have $b=0$ in the former but $b\neq0$ in the latter.

