Question

30 points if you answer this question and please show work !

Answer 1

$h(x)=\dfrac{f(x)}{g(x)}=\dfrac{x^2+x-20}{x+5}=\dfrac{x^2+x+4x-4x-20}{x+5}=\\\\\\= \dfrac{x^2+5x-4x-20}{x+5}=\dfrac{x(x+5)-4(x+5)}{x+5}=\dfrac{(x+5)(x-4)}{x+5}=\\\\\\=\boxed{x-4}$

We see, that g(x) is in denominator, so:

$g(x)\neq0\\\\x+5\neq0\\\\\boxed{x\neq-5}$

and the domain of $h(x)$ is the set of all real numbers without $x=-5$.