Ta có: \(B=\left(\frac{4x}{x+2}+\frac{8x^2}{4-x^2}\right):\left(\frac{x-1}{x^2-2x}-\frac{2}{x}\right)\)
\(=\left(\frac{4x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{8x^2}{\left(x-2\right)\left(x+2\right)}\right):\left(\frac{x-1}{x\left(x-2\right)}-\frac{2\left(x-2\right)}{x\left(x-2\right)}\right)\)
\(=\frac{4x^2-8x-8x^2}{\left(x-2\right)\left(x+2\right)}:\frac{x-1-2x+4}{\left(x-2\right)}\)
\(=\frac{-4x^2-8x}{\left(x-2\right)\left(x+2\right)}\cdot\frac{x-2}{3-x}\)
\(=\frac{-4x\left(x+2\right)}{x+2}\cdot\frac{1}{3-x}\)
\(=-\frac{4x}{3-x}=\frac{4x}{x-3}\)
a) ĐKXĐ: \(x\notin\left\{2;-2;0;3\right\}\)
Để B=-1 thì \(\frac{4x}{x-3}=-1\)
\(\Leftrightarrow4x=3-x\)
\(\Leftrightarrow4x+x=3\)
\(\Leftrightarrow5x=3\)
hay \(x=\frac{3}{5}\)(nhận)
Vậy: Để B=-1 thì \(x=\frac{3}{5}\)
b) Sửa đề: Tìm x để B<0
Để B<0 thì \(\frac{4x}{x-3}< 0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}4x>0\\x-3< 0\end{matrix}\right.\\\left\{{}\begin{matrix}4x< 0\\x-3>0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>0\\x< 3\end{matrix}\right.\\\left\{{}\begin{matrix}x< 0\\x>3\end{matrix}\right.\end{matrix}\right.\Leftrightarrow0< x< 3\)
Kết hợp ĐKXĐ, ta được:
\(\left\{{}\begin{matrix}0< x< 3\\x\ne2\end{matrix}\right.\)
Vậy: Để B<0 thì \(\left\{{}\begin{matrix}0< x< 3\\x\ne2\end{matrix}\right.\)
