Đáp án:
\(\dfrac{{x - 1}}{{\left( {x + 1} \right)\left( {x - 2} \right)}}\)
Giải thích các bước giải:
\(\begin{array}{l}
B = \dfrac{{x - 1}}{{x + 1}}:\left[ {\dfrac{{x + 3}}{{x - 2}} + \dfrac{{x + 2}}{{3 - x}} + \dfrac{{x + 2}}{{{x^2} + 5x + 6}}} \right]\\
= \dfrac{{x - 1}}{{x + 1}}.\left[ {\dfrac{{\left( {x + 3} \right)\left( {x - 3} \right) - \left( {x + 2} \right)\left( {x - 2} \right) + x + 2}}{{\left( {x - 2} \right)\left( {x - 3} \right)}}} \right]\\
= \dfrac{{x - 1}}{{x + 1}}.\dfrac{{{x^2} - 9 - {x^2} + 4 + x + 2}}{{\left( {x - 2} \right)\left( {x - 3} \right)}}\\
= \dfrac{{x - 1}}{{x + 1}}.\dfrac{{x - 3}}{{\left( {x - 2} \right)\left( {x - 3} \right)}}\\
= \dfrac{{x - 1}}{{\left( {x + 1} \right)\left( {x - 2} \right)}}
\end{array}\)
