với điều kiện x#0,x#5,x#-5,x #5/2 thực hiện phép tính sau :(x/(x^2 – 25) – (x – 5)/(x^2 + 5x)) : ((2x – 5)/(x^2 + 5x) – x/(x – 5))

Đáp án:

\(\dfrac{{10x – 25}}{{ – {x^3} – 3{x^2} – 15x + 25}}\)

Giải thích các bước giải:

\(\begin{array}{l}
\left( {\dfrac{x}{{{x^2} – 25}} – \dfrac{{x – 5}}{{{x^2} + 5x}}} \right):\left( {\dfrac{{2x – 5}}{{{x^2} + 5x}} – \dfrac{x}{{x – 5}}} \right)\\
 = \left[ {\dfrac{{{x^2} – {{\left( {x – 5} \right)}^2}}}{{x\left( {x – 5} \right)\left( {x + 5} \right)}}} \right]:\left[ {\dfrac{{\left( {2x – 5} \right)\left( {x – 5} \right) – x\left( {{x^2} + 5x} \right)}}{{x\left( {x – 5} \right)\left( {x + 5} \right)}}} \right]\\
 = \dfrac{{{x^2} – {x^2} + 10x – 25}}{{x\left( {x – 5} \right)\left( {x + 5} \right)}}.\dfrac{{x\left( {x – 5} \right)\left( {x + 5} \right)}}{{2{x^2} – 15x + 25 – {x^3} – 5{x^2}}}\\
 = \dfrac{{10x – 25}}{{ – {x^3} – 3{x^2} – 15x + 25}}
\end{array}\)