ĐKXĐ: \(x\ne-1\)
\(\Leftrightarrow x^2-\frac{2x.x}{x+1}+\frac{x^2}{\left(x+1\right)^2}+\frac{2x^2}{x+1}=15\)
\(\Leftrightarrow\left(x-\frac{x}{x+1}\right)^2+\frac{2x^2}{x+1}-15=0\)
\(\Leftrightarrow\left(\frac{x^2}{x+1}\right)^2+\frac{2x^2}{x+1}-15=0\)
Đặt \(\frac{x^2}{x+1}=a\) phương trình trở thành:
\(a^2+2a-15=0\Rightarrow\left[{}\begin{matrix}a=3\\a=-5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\frac{x^2}{x+1}=3\\\frac{x^2}{x+1}=-5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-3x-3=0\\x^2+5x+5=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{3\pm\sqrt{21}}{2}\\x=\frac{-5\pm\sqrt{5}}{2}\end{matrix}\right.\)
