## College Algebra 7th Edition

$\displaystyle\{x|x\geq 0$ and $x\neq 4\}$
We know that $\displaystyle \frac{\sqrt{x}}{x^{2}-3x-4}$ is undefined whenever the denominator is 0, so: $x^2-3x-4=(x+1)(x-4)=0$ $x=-1, x=4$ The equation is also undefined when taking the square root of a negative number ($x\lt0$). Combining these restrictions, we get the domain: $\{x|x\geq 0$ and $x\neq 4\}$