Question

x-1/x+1/x+1=2x-1/x^2+x

Answer 1

ĐKXĐ:\(\left\{{}\begin{matrix}x\ne0\\x\ne-1\end{matrix}\right.\)

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