Simplify the following by factoring and canceling. \[ \frac{x^{2}-64}{8-x} \]

To simplify the expression \(\frac{x^{2}-64}{8-x}\), we start by factoring the numerator. The expression \(x^{2} - 64\) is a difference of squares, which can be factored into: \[ (x - 8)(x + 8) \] Now, we rewrite the original expression: \[ \frac{x^{2} - 64}{8 - x} = \frac{(x - 8)(x + 8)}{8 - x} \] Notice that \(8 - x\) can be rewritten as \(-(x - 8)\). So we have: \[ \frac{(x - 8)(x + 8)}{-(x - 8)} \] Since \((x - 8)\) appears in both the numerator and the denominator, we can cancel it out—provided that \(x \neq 8\) to avoid division by zero: \[ = - (x + 8) \] Thus, the simplified expression is: \[ -(x + 8) \quad \text{for } x \neq 8 \]