\(\left(x+1+\dfrac{1}{x}\right)^2=\left(x-1-\dfrac{1}{x}\right)^2\left(đk:x\ne0\right)\)
\(\left(x+1+\dfrac{1}{x}\right)^2-\left(x-1-\dfrac{1}{x}\right)^2=0\)
\(\left(x+1+\dfrac{1}{x}+x-1-\dfrac{1}{x}\right)\left(x+1+\dfrac{1}{x}-x+1+\dfrac{1}{x}\right)=0\)
\(2x\left(2+\dfrac{1}{x}+\dfrac{1}{x}\right)=0\)
\(2x\left(\dfrac{2x}{x}+\dfrac{1}{x}+\dfrac{1}{x}\right)=0\)
\(2x\left(2x+2\right)=0\\ \left[{}\begin{matrix}2x=0\\2x+2=0\end{matrix}\right.\\ \left[{}\begin{matrix}x=0\left(loại\right)\\x=-1\left(tmđk\right)\end{matrix}\right.\)
\(\left(x+1+\dfrac{1}{x}\right)^2=\left(x-1-\dfrac{1}{x}\right)^2\)
\(\Leftrightarrow\left(x+1+\dfrac{1}{x}\right)^2-\left(x-1-\dfrac{1}{x}\right)^2=0\)
\(\Leftrightarrow\left[x+1+\dfrac{1}{x}-x+1+\dfrac{1}{x}\right]\left[x+1+\dfrac{1}{x}+x-1-\dfrac{1}{x}\right]=0\)
\(\Leftrightarrow2x\left(2+2\dfrac{1}{2}\right)=0\)
\(\Leftrightarrow2x\left(2+\dfrac{2x+1}{2}\right)0\)
\(\Leftrightarrow2x.\dfrac{4x+1}{2}=0\)
\(\Leftrightarrow2\left(2x+1\right)=0\)
\(\Leftrightarrow x=\dfrac{-1}{2}\)
