1. **State the problem:** Simplify the expression $$\frac{\frac{1}{x} - \frac{1}{y}}{y^2 - x^2}$$ and identify which of the given options (a to e) it equals. 2. **Rewrite the numerator:** $$\frac{1}{x} - \frac{1}{y} = \frac{y - x}{xy}$$ 3. **Rewrite the denominator:** Recall the difference of squares formula: $$y^2 - x^2 = (y - x)(y + x)$$ 4. **Substitute numerator and denominator:** $$\frac{\frac{y - x}{xy}}{(y - x)(y + x)}$$ 5. **Divide the fractions:** $$= \frac{y - x}{xy} \times \frac{1}{(y - x)(y + x)} = \frac{y - x}{xy(y - x)(y + x)}$$ 6. **Cancel common factors:** Since $y - x$ appears in numerator and denominator, cancel it: $$= \frac{\cancel{y - x}}{xy \cancel{(y - x)} (y + x)} = \frac{1}{xy(y + x)}$$ 7. **Rewrite denominator:** $$xy(y + x) = xy(x + y)$$ (since addition is commutative) 8. **Final simplified expression:** $$\frac{1}{xy(x + y)}$$ 9. **Match with options:** Option b is $$\frac{1}{xy(x + y)}$$, which matches our result. **Answer:** b. $$\frac{1}{xy(x + y)}$$