Đáp án:
\(A = \frac{5}{2}\)
Giải thích các bước giải:
\(\begin{array}{l}
A = \frac{{\left( {3x - 2} \right)\left( {x + 1} \right) - \left( {2x + 5} \right)\left( {{x^2} - 1} \right)}}{{x + 1}}\\
A = \frac{{\left( {3x - 2} \right)\left( {x + 1} \right) - \left( {2x + 5} \right)\left( {x + 1} \right)\left( {x - 1} \right)}}{{x + 1}}\\
A = \frac{{\left( {x + 1} \right)\left[ {3x - 2 - \left( {2x + 5} \right)\left( {x - 1} \right)} \right]}}{{x + 1}}\\
A = 3x - 2 - \left( {2x + 5} \right)\left( {x - 1} \right)\\
A = 3x - 2 - 2{x^2} + 2x - 5x + 5\\
A = - 2{x^2} + 3\\
Thay\,\,x = \frac{1}{2}\\
\Rightarrow A = - 2.{\left( {\frac{1}{2}} \right)^2} + 3\\
\,\,\,\,\,A = - 2.\frac{1}{4} + 3\\
\,\,\,\,A = - \frac{1}{2} + 3 = \frac{5}{2}
\end{array}\)
