# How do you find the domain of sqrt(x - 1)/(x + 4)?

Apr 13, 2018

$\left[0 , \infty\right)$

#### Explanation:

The square root must be positive or zero, so

$x - 1 \ge 0 \to x \ge 1$ is part of our domain.

However, we may not have division by zero either:

$x + 4 \ne 0$

$x \ne - 4$

From the first portion of the problem, where we ensure that we only have a positive root, $x = - 4$ is already excluded from the domain, so, this part of the problem only reinforces that $x \ge 0$.

The domain is then $\left[0 , \infty\right)$