a) Factor the numerator and denominator. Do not simplify the common factors. \[ \frac{x^{2}+8 x+7}{x^{2}+5 x-14}=\square \]

To factor the numerator \(x^2 + 8x + 7\), we can look for two numbers that multiply to \(7\) (the constant term) and add to \(8\) (the coefficient of \(x\)). The numbers \(1\) and \(7\) fit the criteria. Thus, the numerator factors to \((x + 1)(x + 7)\). For the denominator \(x^2 + 5x - 14\), we need two numbers that multiply to \(-14\) and add to \(5\). The numbers \(7\) and \(-2\) work for this. Therefore, the denominator factors to \((x + 7)(x - 2)\). Putting it all together, we get: \[ \frac{x^2 + 8x + 7}{x^2 + 5x - 14} = \frac{(x + 1)(x + 7)}{(x + 7)(x - 2)}. \]