To simplify the expression \(\frac{36x - 216}{x^2 - 36}\), we start by factoring both the numerator and the denominator.
-
Factoring the numerator: \[ 36x - 216 = 36(x - 6) \]
-
Factoring the denominator: \[ x^2 - 36 = (x - 6)(x + 6) \quad \text{(This is a difference of squares)} \]
Now, substituting the factored forms into the expression, we have: \[ \frac{36(x - 6)}{(x - 6)(x + 6)} \]
- Canceling the common factor \((x - 6)\) (as long as \(x \neq 6\)): \[ \frac{36}{x + 6} \]
So, the expression in simplest form is: \[ \frac{36}{x + 6} \]
None of the provided options match this result. Thus, it seems there might be a discrepancy between the calculated answer and the provided choices. Would you like to recheck the problem or discuss this further?