## anonymous 5 years ago What is the domain of sqrt x^2+2x-24/x^2-9

1. anonymous

$\sqrt{x^+2x-24/x^2-9}$

2. anonymous

You want to find the numbers/intervals for which the function is valid. For rationals you cannot have zero in the denominator and for square root functions, you can not have a negative number.

3. anonymous

So infinity to infinity?

4. anonymous

Not quite. You need to solve $x^2-9\neq0$ for x. And then $\sqrt{(x^2+2x-24)/(x^2-9)}\ge0$ for x.

5. anonymous

x=3 for the first one and x= -6 x= -4/ x= -3 x=3

6. anonymous

So the domain is $x \neq \pm3 and -6\ge x \ge 4$