Question

\(\left(1-\dfrac{x-1}{x+1}\right)\left(x+2\right)=\dfrac{x+1}{x-1}+\dfrac{x-1}{x+1}\)

Answer 1

ĐKXĐ: \(x\ne\pm1\)

\(\Leftrightarrow\dfrac{2\left(x+2\right)}{x+1}=\dfrac{\left(x+1\right)^2+\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}\)

\(\Leftrightarrow\dfrac{2\left(x+2\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{2x^2+2}{\left(x+1\right)\left(x-1\right)}\)

\(\Leftrightarrow2\left(x+2\right)\left(x-1\right)=2x^2+2\)

\(\Leftrightarrow2x^2+2x-4=2x^2+2\)

\(\Leftrightarrow2x=6\Rightarrow x=3\)