# What is the domain of sx=(x+2)/(sin(x))?

Sep 22, 2016

$x \in \left\{\mathbb{R} - n \pi , n \in \mathbb{Z}\right\}$
$s \left(x\right) = \frac{x + 2}{\sin} \left(x\right) \textcolor{w h i t e}{\text{XXX}} \mathmr{and} x + \frac{2}{\sin} \left(x\right)$ (not clear which is intended)
is defined for all Real values of $x$ except those for which $\sin \left(x\right) = 0$
Therefore the Domain of $s \left(x\right)$ is all Real values excluding integer multiples of $\pi$ (for which $\sin \left(x\right) = 0$).