Question

Решить уравнение, желательно подробно.

Answer 1

$\\|x|={-2\over x+3}\Leftrightarrow \left\{\begin{matrix} {-2\over x+3}> 0\\ \left[ \begin{gathered} x={-2\over x+3}\\ x={2\over x+3} \hfill \\ \end{gathered} \right. \end{matrix}\right \Leftrightarrow \; \; \; \; \left\{\begin{matrix} x<-5\\ \left[ \begin{gathered} x^2+3x+2=0\\ x^2+3x-2=0 \hfill \\ \end{gathered} \right. \end{matrix}\right \Leftrightarrow \; \; \; \; \left\{\begin{matrix} x<-5\\ \left[ \begin{gathered} x^2+3x+2=0\\ x^2+3x-2=0 \hfill \\ \end{gathered} \right. \end{matrix}\right\\ \Leftrightarrow \; \; \; \; \left\{\begin{matrix} x<-5\\ \left[ \begin{gathered} x_1=-1\\ x_2=-2\\ x_3={-3-\sqrt{17}\over2}\\ x_4={-3+\sqrt{17}\over2} \hfill \\ \end{gathered} \right. \end{matrix}\right\\\\ OTBET: x={-3-\sqrt{17}\over2}$