Đáp án:
\(\dfrac{{8{x^2} - 24x - 38}}{{\left( {4{x^2} - 9} \right)\left( {2x + 1} \right)}}\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \left\{ { - \dfrac{3}{2}; - \dfrac{1}{2};\dfrac{3}{2}} \right\}\\
P = \dfrac{2}{{2x + 3}} + \dfrac{3}{{2x + 1}} - \dfrac{{6x + 5}}{{\left( {2x + 3} \right)\left( {2x - 3} \right)}}\\
= \dfrac{{2\left( {2x - 3} \right)\left( {2x + 1} \right) + 3\left( {4{x^2} - 9} \right) - \left( {6x + 5} \right)\left( {2x + 1} \right)}}{{\left( {2x + 3} \right)\left( {2x - 3} \right)\left( {2x + 1} \right)}}\\
= \dfrac{{\left( {2x + 1} \right)\left( {4x - 6} \right) + 12{x^2} - 27 - 12{x^2} - 16x - 5}}{{\left( {2x + 3} \right)\left( {2x - 3} \right)\left( {2x + 1} \right)}}\\
= \dfrac{{8{x^2} - 8x - 6 - 16x - 32}}{{\left( {2x + 3} \right)\left( {2x - 3} \right)\left( {2x + 1} \right)}}\\
= \dfrac{{8{x^2} - 24x - 38}}{{\left( {4{x^2} - 9} \right)\left( {2x + 1} \right)}}
\end{array}\)
