1. **State the problem:** We want to find an expression equivalent to $$\frac{1}{\frac{1}{x+2} + \frac{1}{x+3}}$$ for $$x > 3$$. 2. **Recall the formula for sum of fractions:** $$\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab}$$ 3. **Apply the formula to the denominator:** $$\frac{1}{x+2} + \frac{1}{x+3} = \frac{(x+2)+(x+3)}{(x+2)(x+3)} = \frac{2x+5}{(x+2)(x+3)}$$ 4. **Rewrite the original expression:** $$\frac{1}{\frac{2x+5}{(x+2)(x+3)}}$$ 5. **Simplify by dividing by a fraction:** $$= 1 \times \frac{(x+2)(x+3)}{2x+5} = \frac{(x+2)(x+3)}{2x+5}$$ 6. **Expand the numerator:** $$ (x+2)(x+3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6 $$ 7. **Final simplified expression:** $$\frac{x^2 + 5x + 6}{2x + 5}$$ **Answer:** Option B