Question

the function h is defined below.\\( h(x)=\frac{x^2 + 2x - 63}{x^2 + 18x + 81} \\)\
find all values of x that are not in the domain of h.\
if there is more than one value, separate them with commas.\
\\( x = \square \\)

Explanation:

Step1: Identify undefined condition

A rational function is undefined when its denominator equals 0. So set the denominator equal to 0:
$x^2 + 18x + 81 = 0$

Step2: Factor the quadratic

Factor the perfect square trinomial:
$(x + 9)^2 = 0$

Step3: Solve for x

Solve the factored equation:
$x + 9 = 0 \implies x = -9$

Answer:

$x = -9$