Simplify the following by factoring and canceling. \[ \frac{x^{2}-9}{3-x} \]

To simplify the expression \(\frac{x^{2}-9}{3-x}\), we start by factoring the numerator. The expression \(x^{2} - 9\) is a difference of squares, which can be factored as: \[ x^{2} - 9 = (x - 3)(x + 3) \] Now we rewrite the original expression using this factorization: \[ \frac{x^{2}-9}{3-x} = \frac{(x - 3)(x + 3)}{3 - x} \] Next, we can notice that \(3 - x\) can be rewritten as \(-(x - 3)\). Therefore, we replace \(3 - x\) in the denominator: \[ \frac{(x - 3)(x + 3)}{-(x - 3)} = -\frac{(x - 3)(x + 3)}{(x - 3)} \] Assuming \(x \neq 3\) (to avoid division by zero), we can cancel the \(x - 3\) from the numerator and denominator: \[ - (x + 3) \] So the expression simplifies to: \[ -(x + 3) = -x - 3 \] Therefore, the simplified expression is: \[ -x - 3 \]