Question

\(\dfrac{x}{x+1}\)+2=x

Answer 1

ĐKXĐ: \(x\ne-1\)

\(\dfrac{x}{x+1}+2=x\\ \Leftrightarrow\dfrac{x}{x+1}=x-2\\ \Leftrightarrow x=\left(x-2\right)\left(x+1\right)\\ \Leftrightarrow x=x^2-x-2\\ \Leftrightarrow x^2-2x-2=0\\ \Leftrightarrow\left(x^2-2x+1\right)-3=0\\ \Leftrightarrow\left(x-1\right)^2-\sqrt{3^2}=0\\ \Leftrightarrow\left(x-1-\sqrt{3}\right)\left(x-1+\sqrt{3}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1+\sqrt{3}\left(tm\right)\\x=1-\sqrt{3}\left(tm\right)\end{matrix}\right.\)