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