1. **State the problem:** Simplify the expression $$\frac{5 - \sqrt{18}}{1 - \sqrt{2}}$$ and write it in the form $$a + b\sqrt{2}$$ where $$a$$ and $$b$$ are integers. 2. **Recall the formula:** To simplify expressions with radicals in the denominator, multiply numerator and denominator by the conjugate of the denominator. The conjugate of $$1 - \sqrt{2}$$ is $$1 + \sqrt{2}$$. 3. **Multiply numerator and denominator by the conjugate:** $$\frac{5 - \sqrt{18}}{1 - \sqrt{2}} \times \frac{1 + \sqrt{2}}{1 + \sqrt{2}} = \frac{(5 - \sqrt{18})(1 + \sqrt{2})}{(1 - \sqrt{2})(1 + \sqrt{2})}$$ 4. **Simplify the denominator using difference of squares:** $$ (1)^2 - (\sqrt{2})^2 = 1 - 2 = -1 $$ 5. **Expand the numerator:** $$ (5)(1) + (5)(\sqrt{2}) - (\sqrt{18})(1) - (\sqrt{18})(\sqrt{2}) = 5 + 5\sqrt{2} - \sqrt{18} - \sqrt{36} $$ 6. **Simplify the radicals:** $$ \sqrt{18} = 3\sqrt{2}, \quad \sqrt{36} = 6 $$ 7. **Substitute back:** $$ 5 + 5\sqrt{2} - 3\sqrt{2} - 6 = (5 - 6) + (5\sqrt{2} - 3\sqrt{2}) = -1 + 2\sqrt{2} $$ 8. **Put numerator and denominator together:** $$ \frac{-1 + 2\sqrt{2}}{-1} = \frac{-1}{-1} + \frac{2\sqrt{2}}{-1} = 1 - 2\sqrt{2} $$ **Final answer:** $$1 - 2\sqrt{2}$$ where $$a = 1$$ and $$b = -2$$.