tính A=(x/x^2-25-x-5/x^2+ 5 x): (2 x-5/x^2+ 5 x) +x/5-x

Đáp án:

\[ – 1\]

Giải thích các bước giải:

\(\begin{array}{l}
A = \left( {\frac{x}{{{x^2} – 25}} – \frac{{x – 5}}{{{x^2} + 5x}}} \right):\left( {\frac{{2x – 5}}{{{x^2} + 5x}}} \right) + \frac{x}{{5 – x}}\\
 = \left( {\frac{x}{{\left( {x – 5} \right)\left( {x + 5} \right)}} – \frac{{\left( {x – 5} \right)}}{{x\left( {x + 5} \right)}}} \right):\left( {\frac{{2x – 5}}{{x\left( {x + 5} \right)}}} \right) + \frac{x}{{5 – x}}\\
 = \left( {\frac{{{x^2} – {{\left( {x – 5} \right)}^2}}}{{x\left( {x – 5} \right)\left( {x + 5} \right)}}} \right):\frac{{2x – 5}}{{x\left( {x + 5} \right)}} + \frac{x}{{5 – x}}\\
 = \frac{{10x – 25}}{{x\left( {x – 5} \right)\left( {x + 5} \right)}}.\frac{{x\left( {x + 5} \right)}}{{2x – 5}} + \frac{x}{{5 – x}}\\
 = \frac{5}{{x – 5}} – \frac{x}{{x – 5}}\\
 = \frac{{5 – x}}{{x – 5}} =  – 1
\end{array}\)