Step-by-step explanation:
[tex] \frac{1}{ \frac{1}{x + 2} + \frac{1}{x + 3} } \\ \\ = \frac{1}{ \frac{x + 3 + x + 2}{(x + 3)(x + 2)} } \\ \\ = \frac{1}{ \frac{2x + 5 }{ {x}^{2} + 2x + 3x + 6 } } \\ \\ = \frac{1}{ \frac{2x + 5 }{ {x}^{2} + 5x + 6 } } \\ \\ = \frac{{x}^{2} + 5x + 6}{2x + 5} \\ [/tex]
Thus, option B is the correct answer.
