# How do you find the domain of sqrt(x+4)/(x-3)?

Oct 31, 2017

D: [-4, 3) $\cup$ (3, $\infty$)

#### Explanation:

You would find the domain of the numerator and the domain of the denominator, see if there are any intersections, and then write the answer in interval notation. The numerator is a square root, so whatever is inside must be positive. So, you have $x + 4 \ge 0$, which solves to see that $x$ must be greater than or equal to -4. In the denominator, you can't get 0, as this will evaluate to undefined. So, if $x - 3 = 0$, you see that $x$ can't equal 3. So, in interval notation, you show that $x$ must be greater than or equal to -4, but not equal to 3.

Nov 5, 2017

$x \in \mathbb{R} , x \ne 3$

#### Explanation:

$\text{the denominator of the rational function cannot be}$
$\text{zero as this would make it "color(blue)"undefined}$

$\text{Equating the denominator to zero and solving gives the}$
$\text{value that x cannot be}$

$\text{solve "x-3=0rArrx=3larrcolor(red)"excluded value}$

$\text{domain is } x \in \mathbb{R} , x \ne 3$