Đáp án:
\[ - 1\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
A = \left( {\frac{x}{{{x^2} - 25}} - \frac{{x - 5}}{{{x^2} + 5x}}} \right):\left( {\frac{{2x - 5}}{{{x^2} + 5x}}} \right) + \frac{x}{{5 - x}}\\
= \left( {\frac{x}{{\left( {x - 5} \right)\left( {x + 5} \right)}} - \frac{{\left( {x - 5} \right)}}{{x\left( {x + 5} \right)}}} \right):\left( {\frac{{2x - 5}}{{x\left( {x + 5} \right)}}} \right) + \frac{x}{{5 - x}}\\
= \left( {\frac{{{x^2} - {{\left( {x - 5} \right)}^2}}}{{x\left( {x - 5} \right)\left( {x + 5} \right)}}} \right):\frac{{2x - 5}}{{x\left( {x + 5} \right)}} + \frac{x}{{5 - x}}\\
= \frac{{10x - 25}}{{x\left( {x - 5} \right)\left( {x + 5} \right)}}.\frac{{x\left( {x + 5} \right)}}{{2x - 5}} + \frac{x}{{5 - x}}\\
= \frac{5}{{x - 5}} - \frac{x}{{x - 5}}\\
= \frac{{5 - x}}{{x - 5}} = - 1
\end{array}\)
