1. **State the problem:** Simplify the expression $$\frac{\sqrt{5}-\sqrt{6}}{\sqrt{18}}$$. 2. **Recall the formula and rules:** To simplify expressions with square roots, we often rationalize the denominator or simplify the radicals. 3. **Simplify the denominator:** $$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$$. 4. **Rewrite the expression:** $$\frac{\sqrt{5}-\sqrt{6}}{3\sqrt{2}}$$. 5. **Rationalize the denominator:** Multiply numerator and denominator by $$\sqrt{2}$$ to eliminate the radical in the denominator: $$\frac{\sqrt{5}-\sqrt{6}}{3\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{(\sqrt{5}-\sqrt{6})\sqrt{2}}{3 \cancel{\sqrt{2}} \cancel{\sqrt{2}}} = \frac{\sqrt{2}\sqrt{5} - \sqrt{2}\sqrt{6}}{3 \times 2}$$ 6. **Simplify the numerator:** $$\sqrt{2}\sqrt{5} = \sqrt{10}$$ $$\sqrt{2}\sqrt{6} = \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$$ So numerator becomes $$\sqrt{10} - 2\sqrt{3}$$. 7. **Write the final simplified expression:** $$\frac{\sqrt{10} - 2\sqrt{3}}{6}$$. **Answer:** $$\boxed{\frac{\sqrt{10} - 2\sqrt{3}}{6}}$$