Đáp án:
$\begin{array}{l}
P = \left( {\frac{{5x + 2}}{{x - 10}} + \frac{{5x - 2}}{{x + 10}}} \right).\frac{{{x^2} - 100}}{{{x^2} + 4}}\\
a)Dkxd:\left\{ \begin{array}{l}
x \ne 10\\
x \ne - 10
\end{array} \right. \Rightarrow x \ne \pm 10\\
b)P = \left( {\frac{{5x + 2}}{{x - 10}} + \frac{{5x - 2}}{{x + 10}}} \right).\frac{{{x^2} - 100}}{{{x^2} + 4}}\\
= \frac{{\left( {5x + 2} \right)\left( {x + 10} \right) + \left( {5x - 2} \right)\left( {x - 10} \right)}}{{\left( {x + 10} \right)\left( {x - 10} \right)}}.\frac{{\left( {x + 10} \right)\left( {x - 10} \right)}}{{{x^2} + 4}}\\
= \frac{{5{x^2} + 50x + 2x + 20 + 5{x^2} - 50x - 2x + 20}}{{{x^2} + 4}}\\
= \frac{{10{x^2} + 40}}{{{x^2} + 4}}\\
= \frac{{10\left( {{x^2} + 4} \right)}}{{{x^2} + 4}}\\
= 10\\
c)P = 10\,\forall x\\
\Rightarrow Khi\,x = 20040 \Rightarrow P = 10
\end{array}$
