Question

giải pt chứa trị tuyệt đối \(\left|\frac{-2m-3}{m+1}\right|=\left|2m+3\right|\)

Answer 1

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\(\Leftrightarrow\left|\frac{2m+3}{m+1}\right|=\left|2m+3\right|\)

\(\Leftrightarrow\left|2m+3\right|\left(\frac{1}{\left|m+1\right|}-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left|2m+3\right|=0\\\frac{1}{\left|m+1\right|}=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2m+3=0\\m+1=1\\m+1=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}m=-\frac{3}{2}\\m=0\\m=-2\end{matrix}\right.\)