1. **State the problem:** Simplify the expression $$\frac{3}{7 - \sqrt{2}}$$. 2. **Formula and rule:** To simplify a fraction with a radical in the denominator, multiply numerator and denominator by the conjugate of the denominator. The conjugate of $$7 - \sqrt{2}$$ is $$7 + \sqrt{2}$$. 3. **Multiply numerator and denominator by the conjugate:** $$\frac{3}{7 - \sqrt{2}} \times \frac{7 + \sqrt{2}}{7 + \sqrt{2}} = \frac{3(7 + \sqrt{2})}{(7 - \sqrt{2})(7 + \sqrt{2})}$$ 4. **Simplify the denominator using difference of squares:** $$ (7)^2 - (\sqrt{2})^2 = 49 - 2 = 47 $$ 5. **Write the expression:** $$ \frac{3(7 + \sqrt{2})}{47} = \frac{21 + 3\sqrt{2}}{47} $$ 6. **Final answer:** $$ \boxed{\frac{21 + 3\sqrt{2}}{47}} $$ This is the simplified form with no radical in the denominator.