Question

Giải pt sau đây:

\(\frac{1}{x-2}-\frac{x^2-4x}{4-x^2}=0\)

Answer 1

ĐK: \(x\ne\pm2\)

\(pt\Rightarrow x+2+x^2-4x=0\Leftrightarrow x^2-3x+2=0\Leftrightarrow x^2-x-2x+2=0\Leftrightarrow x\left(x-1\right)-2\left(x-1\right)=0\Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(L\right)\\x=1\left(N\right)\end{matrix}\right.\)

Vậy \(S=\left\{1\right\}\)