Đáp án:
\[x = - 1\]
Giải thích các bước giải:
ĐKXĐ: \(\left\{ \begin{array}{l}
x \ne - \frac{1}{2}\\
x \ne 3
\end{array} \right.\)
Ta có:
\(\begin{array}{l}
\frac{x}{{2x + 1}} - \frac{2}{{x - 3}} = \frac{{{x^2} + 5}}{{2{x^2} - 5x - 3}}\\
\Leftrightarrow \frac{{x\left( {x - 3} \right) - 2\left( {2x + 1} \right)}}{{\left( {2x + 1} \right)\left( {x - 3} \right)}} = \frac{{{x^2} + 5}}{{\left( {2x + 1} \right)\left( {x - 3} \right)}}\\
\Leftrightarrow \frac{{{x^2} - 3x - 4x - 2}}{{\left( {2x + 1} \right)\left( {x - 3} \right)}} = \frac{{{x^2} + 5}}{{\left( {2x + 1} \right)\left( {x - 3} \right)}}\\
\Leftrightarrow {x^2} - 7x - 2 = {x^2} + 5\\
\Leftrightarrow - 7x - 7 = 0\\
\Leftrightarrow x = - 1\,\,\,\left( {t/m} \right)
\end{array}\)
Vậy \(x = - 1\)
