Simplify \(\frac{1 + \sqrt{8}}{3 - \sqrt{2}}\).

To simplify the given expression, we need to eliminate the square root from the denominator. We can do this by rationalizing the denominator. To do this, we multiply both the numerator and the denominator of the fraction by the conjugate of the denominator. The conjugate of \(3 - \sqrt{2}\) is \(3 + \sqrt{2}\). \begin{align*} \frac{1 + \sqrt{8}}{3 - \sqrt{2}} &= \frac{1 + \sqrt{8}}{3 - \sqrt{2}} \times \frac{3 + \sqrt{2}}{3 + \sqrt{2}}\\ &= \frac{(1 + \sqrt{8})(3 + \sqrt{2})}{(3 - \sqrt{2})(3 + \sqrt{2})}\\ &= \frac{3 + \sqrt{2} + 4\sqrt{2} + 2\sqrt{2}}{7}\\ &= \frac{5\sqrt{2} + 3 + \sqrt{2}}{7}\\ &= \frac{8\sqrt{2} + 3}{7} \end{align*} Therefore, the simplified form of the expression is \(\frac{8\sqrt{2} + 3}{7}\), which corresponds to option (D).