Question

find the domain of the following rational function.$h(x)=\frac{-9x^{2}}{(x-3)(x+8)}$select the correct choice below and, if necessary, fill in the answer box to complete your choice.a. the domain of h(x) is {x | $\boldsymbol{\square}$}.(type an inequality in the form x ≠ . use integers or fractions for any numbers in the expression. use a comma to sepab. the domain of h(x) is the set of all real numbers.

Explanation:

Step1: Identify denominator roots

Set denominator equal to 0:
$$(x-3)(x+8)=0$$
Solve for $x$: $x-3=0 \implies x=3$; $x+8=0 \implies x=-8$

Step2: Exclude roots from domain

Rational functions are undefined where denominator is 0, so exclude $x=3$ and $x=-8$.

Answer:

A. The domain of H(x) is {x | $x
eq 3, -8$}.