Đáp án:
\(P = - \dfrac{2}{{x - 2}}\)
Giải thích các bước giải:
\(\begin{array}{l}
A = x\left( {x - 5} \right) - \dfrac{{x - 5}}{{{x^2} - 25}}\\
= x\left( {x - 5} \right) - \dfrac{{x - 5}}{{\left( {x - 5} \right)\left( {x + 5} \right)}}\\
= x\left( {x - 5} \right) - \dfrac{1}{{x + 5}} = \dfrac{{x\left( {x - 5} \right)\left( {x + 5} \right) - 1}}{{x + 5}}\\
= \dfrac{{x\left( {{x^2} - 25} \right) - 1}}{{x + 5}} = \dfrac{{{x^3} - 25x - 1}}{{x + 5}}\\
P = \dfrac{2}{{x - 2}} + \dfrac{1}{{x + 2}} + \dfrac{{6 + 5x}}{{4 - {x^2}}}\\
= \dfrac{{2\left( {x + 2} \right) + x - 2 - 6 - 5x}}{{\left( {x + 2} \right)\left( {x - 2} \right)}}\\
= \dfrac{{2x + 4 + x - 2 - 6 - 5x}}{{\left( {x + 2} \right)\left( {x - 2} \right)}}\\
= \dfrac{{ - 2x - 4}}{{\left( {x + 2} \right)\left( {x - 2} \right)}} = - \dfrac{2}{{x - 2}}
\end{array}\)
