92. \( f(x)=\frac{x^{2}-16}{x+4} \)

We start with the function   f(x) = (x² – 16) / (x + 4). Step 1. Factor the numerator:   x² – 16 is a difference of two squares, so it factors as     x² – 16 = (x – 4)(x + 4). Step 2. Substitute the factored form back into the function:   f(x) = [(x – 4)(x + 4)] / (x + 4). Step 3. Cancel the common factor:   The factor (x + 4) cancels from the numerator and the denominator, but note that cancellation is only valid if (x + 4) ≠ 0. Therefore, x must not equal –4.   After canceling, we have     f(x) = x – 4  (for x ≠ –4). Step 4. Domain and interpretation:   The simplified expression is f(x) = x – 4 for all x except x = –4. Although the algebra simplifies to a linear function, the original function is not defined at x = –4 because it would cause division by zero.   Graphically, this means that the graph of f(x) is the line y = x – 4 with a hole (a removable discontinuity) at x = –4. Final Answer:   The function simplifies to f(x) = x – 4 for x ≠ –4.