Question

Giải phương trình:

\(\frac{x^2-x}{x^2-x+1}-\frac{x^2-x+2}{x^2-x-2}=1\)

Answer 1

ĐKXĐ: ...

Đặt \(x^2-x=t\) ta được:

\(\frac{t}{t+1}-\frac{t+2}{t-2}=1\)

\(\Leftrightarrow t\left(t-2\right)-\left(t+2\right)\left(t+1\right)=\left(t+1\right)\left(t-2\right)\)

\(\Leftrightarrow t^2+4t=0\Rightarrow\left[{}\begin{matrix}t=0\\t=-4\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x^2-x=0\\x^2-x=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x\left(x-1\right)=0\\\left(x-\frac{1}{2}\right)^2+\frac{15}{4}=0\left(vn\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)