ĐKXĐ: \(x\ne-1\)
\(\frac{x^2+x^2}{\left(x+1\right)^2}=1\)<=>\(\frac{2x^2}{\left(x+1\right)^2}-\frac{\left(x+1\right)^2}{\left(x+1\right)^2}=0\)<=>\(\frac{2x^2-\left(x+1\right)^2}{\left(x+1\right)^2}=0\)<=>\(\frac{2x^2-\left(x^2+2x+1\right)}{\left(x+1\right)^2}=0\)
<=>\(\frac{2x^2-x^2-2x-1}{\left(x+1\right)^2}=0\)<=>\(\frac{x^2-2x-1}{\left(x+1\right)^2}=0\)
\(\left(x+1\right)^2\ne0\)<=> \(x^2-2x-1=0\Leftrightarrow x^2-2x+1-2=0\Leftrightarrow\left(x-1\right)^2-2=0\)
<=>\(\left(x-1\right)^2=2\)<=>\(x-1=\left[\begin{array}{nghiempt}-\sqrt{2}\\\sqrt{2}\end{array}\right.\)<=>\(x=\left[\begin{array}{nghiempt}-\sqrt{2}+1\\\sqrt{2}+1\end{array}\right.\)
\(\frac{x^2+x^2}{\left(x+1\right)^2}=\frac{x^2+x^2}{x^2+2x.1+1^2}=\frac{2x^2}{x^2+2x+1}=\frac{2}{2x+1}=\frac{1}{x+1}\)
