Final answer:
To find the x values that are not in the domain of h(x) = (x - 5)/(x² + 15x + 54), we can use the quadratic formula.
Step-by-step explanation:
The given function is h(x) = (x - 5)/(x² + 15x + 54). To find the x values that are not in the domain, we need to identify the values of x that make the denominator zero. In this case, the denominator is x² + 15x + 54. We can use the quadratic formula to find the values of x that make the denominator zero.
The quadratic formula is x = (-b ± √(b² - 4ac))/(2a). By substituting the values of a, b, and c from the expression x² + 15x + 54 into the quadratic formula, we get:
x = (-15 ± √(15² - 4(1)(54)))/(2(1))
Simplifying further, we get:
x = (-15 ± √(225 - 216))/2
x = (-15 ± √9)/2
x = (-15 ± 3)/2
Therefore, the x values that are not in the domain of h(x) are 6 and -9.