Answer: x = 5 and x = -3.
Explanation:
To find the zeros of the function H(x) = (x^2 - 2x - 15) / (x^2 - 9), we need to find the values of x that make the numerator equal to zero, since dividing by zero is undefined.
Step 1: Set the numerator equal to zero and solve for x:
x^2 - 2x - 15 = 0
Step 2: Factor the quadratic equation:
(x - 5)(x + 3) = 0
Step 3: Apply the zero product property:
x - 5 = 0 or x + 3 = 0
Step 4: Solve for x:
For x - 5 = 0, add 5 to both sides:
x = 5
For x + 3 = 0, subtract 3 from both sides:
x = -3
The zeros of the function H(x) are x = 5 and x = -3. These are the values of x that make the numerator equal to zero, and dividing by zero is undefined in this case.