Đáp án:
\(\left[ \begin{array}{l}
x = 4,201472338\\
x = 0,5450959088\\
x = - 1,746568247
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \left\{ { - 1;0;1} \right\}\\
Pt \to \frac{{\left( {x + 1} \right)\left( {x - 1} \right) - 2x}}{{x\left( {x - 1} \right)}} = \frac{{\left( {2x + 5} \right)\left( {x - 1} \right)}}{{x\left( {x - 1} \right)\left( {x + 1} \right)}}\\
\to \frac{{\left( {{x^2} - 1} \right)\left( {x + 1} \right) - 2x\left( {x + 1} \right)}}{{x\left( {x - 1} \right)\left( {x + 1} \right)}} = \frac{{2{x^2} - 2x + 5x - 5}}{{x\left( {x - 1} \right)\left( {x + 1} \right)}}\\
\to {x^3} + {x^2} - x - 1 - 2{x^2} - 2x = 2{x^2} + 3x - 5\\
\to {x^3} - 3{x^2} - 6x + 4 = 0\\
\to \left[ \begin{array}{l}
x = 4,201472338\\
x = 0,5450959088\\
x = - 1,746568247
\end{array} \right.
\end{array}\)
