Đáp án:

\(\dfrac{{2 - x}}{{x - 4}}\)

Giải thích các bước giải:

\(\begin{array}{l}
\left( {\dfrac{x}{{{x^2} - 16}} - \dfrac{{x - 4}}{{{x^2} + 4x}}} \right):\left( {\dfrac{{4x - 8}}{{{x^2} + 4x}}} \right) + \dfrac{x}{{4 - x}}\\
 = \dfrac{{{x^2} - {{\left( {x - 4} \right)}^2}}}{{x\left( {x - 4} \right)\left( {x + 4} \right)}}.\dfrac{{x\left( {x + 4} \right)}}{{4\left( {x - 2} \right)}} - \dfrac{x}{{x - 4}}\\
 = \dfrac{{{x^2} - {x^2} + 8x - 16}}{{x\left( {x - 4} \right)\left( {x + 4} \right)}}.\dfrac{{x\left( {x + 4} \right)}}{{4\left( {x - 2} \right)}} - \dfrac{x}{{x - 4}}\\
 = \dfrac{{8\left( {x - 2} \right)}}{{x\left( {x - 4} \right)\left( {x + 4} \right)}}.\dfrac{{x\left( {x + 4} \right)}}{{4\left( {x - 2} \right)}} - \dfrac{x}{{x - 4}}\\
 = \dfrac{2}{{x - 4}} - \dfrac{x}{{x - 4}} = \dfrac{{2 - x}}{{x - 4}}
\end{array}\)

Đáp án:

`↓↓` 

Giải thích các bước giải:

`(x/(x^2-16)-(x-4)/(x^2+4x)):((4x-8)/(x^2+4x))+x/(4-x)`

`=(x/((x-4)(x+4))-(x-4)/(x(x+4)):((4x-8)/(x(x+4))+x/(4-x)`

`=((x^2)/(x(x-4)(x+4)) - ((x-4)^2)/(x(x-4)(x+4))):(4x-8)/(x(x+4))+x/(4-x)`

`=(x^2-(x-4)^2)/(x(x-4)(x+4))  . (x(x+4))/(4x-8) +x/(4-x)`

`=(8(x-2))/(x(x-4)(x+4))  . (x(x+4))/(4(x-2))+x/(4-x)`

`=2/(x-4) - x/(x-4)`

`=(2-x)/(x-4)`