Answer
$D=\{x|-5\leqslant x<5\}=[-5, 5)$
Work Step by Step
$g(x)=\sqrt {\frac{5+x}{5-x}}$,
To get the domain,
$g(x)=\frac{\sqrt{5+x}}{\sqrt{5-x}}$,
First solving for the numerator, $\sqrt{5+x}\geqslant 0, 5+x\geq 0, x\geq-5$.
And then solving for the denominator, $\sqrt{5-x}\gt0, 5-x\gt0, x\lt5$.
Therefore the Domain is:
$D=\{x|-5\leqslant x<5\}= [-5, 5)$
