1. The problem is to simplify the expression $$\left| \frac{1}{\sqrt{54}} - \frac{1}{\sqrt{50}} \right|$$. 2. First, simplify the square roots in the denominators: $$\sqrt{54} = \sqrt{9 \times 6} = 3\sqrt{6}$$ $$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$$ 3. Substitute these back into the expression: $$\left| \frac{1}{3\sqrt{6}} - \frac{1}{5\sqrt{2}} \right|$$ 4. To subtract these fractions, find a common denominator: The common denominator is $$15\sqrt{6}\sqrt{2} = 15\sqrt{12}$$. 5. Rewrite each fraction with the common denominator: $$\frac{1}{3\sqrt{6}} = \frac{5\sqrt{2}}{15\sqrt{12}}$$ $$\frac{1}{5\sqrt{2}} = \frac{3\sqrt{6}}{15\sqrt{12}}$$ 6. Now subtract the numerators: $$\left| \frac{5\sqrt{2} - 3\sqrt{6}}{15\sqrt{12}} \right|$$ 7. Simplify $$\sqrt{12}$$: $$\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$$ 8. Substitute back: $$\left| \frac{5\sqrt{2} - 3\sqrt{6}}{15 \times 2 \sqrt{3}} \right| = \left| \frac{5\sqrt{2} - 3\sqrt{6}}{30\sqrt{3}} \right|$$ 9. This is the simplified form of the original expression. Final answer: $$\boxed{\left| \frac{5\sqrt{2} - 3\sqrt{6}}{30\sqrt{3}} \right|}$$