# How do you find the domain of sqrt(x+1)/(x-9)?

First of all it should be $x + 1 \ge 0 \implies x \ge - 1$ and $x - 9 \ne 0 \implies x \ne 9$
Hence the domain is $D = \left[- 1 , 9\right) U \left(9 , + \infty\right)$
where $U$ is the union of the two sets