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

Rationalizing by multiplying through with \(3 + \sqrt{2}\),

\((\frac{1 + \sqrt{8}}{3 - \sqrt{2}})(\frac{3 + \sqrt{2}}{3 + \sqrt{2}}) = \frac{3 + \sqrt{2} + 3\sqrt{8} + 4}{9 - 2}\)

= \(\frac{3 + \sqrt{2} + 3\sqrt{4 \times 2} + 4}{7} \)

= \(\frac{7 + 7\sqrt{2}}{7} = 1 + \sqrt{2}\)