\(\left(1-\frac{x-1}{x+1}\right)\left(x+2\right)=\frac{x+1}{x-1}+\frac{x-1}{x+1} \) (x\(\ne\pm1\))
\(\frac{x+1-x+1}{x+1}\left(x+2\right)=\frac{\left(x+1\right)^2+\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}\)
\(\Leftrightarrow\frac{2}{x+1}\left(x+2\right)=\frac{x^2+2x+1+x^2-2x+1}{\left(x-1\right)\left(x+1\right)}\)
\(\Leftrightarrow\frac{2\left(x+2\right)}{x+1}=\frac{2x^2+2}{\left(x-1\right)\left(x+1\right)}\)
\(\Leftrightarrow\frac{2\left(x+2\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}-\frac{2x^2+2}{\left(x-1\right)\left(x+1\right)}=0\)
\(\Leftrightarrow\frac{2x^2+x-2-2x^2-2}{\left(x-1\right)\left(x+1\right)}=0\)
\(\Leftrightarrow\frac{x-4}{\left(x-1\right)\left(x+1\right)}=0\)
\(\Rightarrow x=4\left(tm\right)\)
KL:.......