Simplify \[ \frac{3-x}{x^{2}+4 x-21} \] \( \frac{3-x}{x^{2}+4 x-21}=\square \)

To simplify the expression \(\frac{3-x}{x^{2}+4 x-21}\), we start by factoring the denominator. The quadratic \(x^2 + 4x - 21\) can be factored by finding two numbers that multiply to -21 and add to 4. These numbers are 7 and -3. Thus, we can rewrite the denominator as: \[ x^2 + 4x - 21 = (x + 7)(x - 3). \] Now, the expression becomes: \[ \frac{3-x}{(x + 7)(x - 3)}. \] Next, we notice that \(3 - x\) can be rewritten as \(-(x - 3)\), allowing us to simplify the expression further: \[ \frac{3-x}{(x + 7)(x - 3)} = \frac{-(x - 3)}{(x + 7)(x - 3)}. \] We can cancel \(x - 3\) from the numerator and the denominator (assuming \(x \neq 3\)): \[ = \frac{-1}{x + 7}. \] So the simplified expression is: \[ \frac{3-x}{x^{2}+4 x-21} = \frac{-1}{x + 7}. \]