Đáp án:
\(x = \dfrac{3}{{70}}\)
Giải thích các bước giải:
\(\begin{array}{l}
e)x \ne \pm 2y\\
\left\{ \begin{array}{l}
\dfrac{{ - 12}}{{x - 2y}} - \dfrac{4}{{x + 2y}} = - 6\\
\dfrac{3}{{x - 2y}} + \dfrac{4}{{x + 2y}} = - 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{ - 12 + 3}}{{x - 2y}} = - 7\\
\dfrac{3}{{x - 2y}} + \dfrac{4}{{x + 2y}} = - 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
- 9 = - 7x + 14y\\
\dfrac{3}{{x - 2y}} + \dfrac{4}{{x + 2y}} = - 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{7x - 9}}{{14}}\\
\dfrac{3}{{x - 2.\dfrac{{7x - 9}}{{14}}}} + \dfrac{4}{{x + 2.\dfrac{{7x - 9}}{{14}}}} = - 1\left( 1 \right)
\end{array} \right.\\
\left( 1 \right) \to \dfrac{3}{{x - \dfrac{{7x - 9}}{7}}} + \dfrac{4}{{x + \dfrac{{7x - 9}}{7}}} = - 1\\
\to \dfrac{3}{{\dfrac{{7x - 7x + 9}}{7}}} + \dfrac{4}{{\dfrac{{7x + 7x - 9}}{7}}} = - 1\\
\to 3:\dfrac{9}{7} + 4:\left( {\dfrac{{14x - 9}}{7}} \right) = - 1\\
\to 4:\left( {\dfrac{{14x - 9}}{7}} \right) = - \dfrac{{10}}{3}\\
\to \dfrac{{14x - 9}}{7} = - \dfrac{6}{5}\\
\to 14x - 9 = - \dfrac{{42}}{5}\\
\to x = \dfrac{3}{{70}} \to y = - \dfrac{{87}}{{140}}
\end{array}\)
