Question

giải phương trình

\(\dfrac{3}{|x+1|}\) + \(\dfrac{|x+1|}{3}\) = 2

Answer 1

\(\dfrac{3}{\left|x+1\right|}+\dfrac{\left|x+1\right|}{3}=2\) (đk x khác -1)

\(\Leftrightarrow\dfrac{9+\left(\left|x+1\right|\right)^2}{3\left|x+1\right|}=2\)

\(\Leftrightarrow9+\left(\left|x+1\right|\right)^2=6\left|x+1\right|\)

\(\Leftrightarrow\left(\left|x+1\right|\right)^2-6\left|x+1\right|+9=0\)

\(\Leftrightarrow\left(\left|x+1\right|-3\right)^2=0\)

\(\Leftrightarrow\left|x+1\right|-3=0\)

\(\Leftrightarrow\left|x+1\right|=3\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=3\\x+1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-4\end{matrix}\right.\)