Rút gọn biểu thức \(B=\left(\dfrac{1}{x-2}-\dfrac{2x}{4-x^2}+\dfrac{1}{2+x}\right).\left(\dfrac{2}{x}-1\right)\) trong điều kiện xác định của nó, ta được kết quả là
\(B=-\dfrac{1}{x+2}.\)\(B=\dfrac{1}{x+2}.\)\(B=\dfrac{4}{x+2}.\)\(B=-\dfrac{4}{x+2}.\)Hướng dẫn giải:\(B=\left(\dfrac{1}{x-2}-\dfrac{2x}{4-x^2}+\dfrac{1}{2+x}\right).\left(\dfrac{2}{x}-1\right)\)
\(=\left(\dfrac{1}{x-2}+\dfrac{2x}{\left(x-2\right)\left(x+2\right)}+\dfrac{1}{x+2}\right).\left(\dfrac{2}{x}-\dfrac{x}{x}\right)\)
\(=\left(\dfrac{x+2}{\left(x-2\right)\left(x+2\right)}+\dfrac{2x}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}\right).\dfrac{2-x}{x}\)
\(=\dfrac{x+2+2x+x-2}{\left(x-2\right)\left(x+2\right)}.\dfrac{2-x}{x}\)
\(=\dfrac{4x}{\left(x-2\right)\left(x+2\right)}.\dfrac{2-x}{x}=-\dfrac{4}{x+2}.\)
