Cho biết \(\dfrac{x^2+3x}{x-1}.Q=\dfrac{x^2-9}{x^2-x}\). Khẳng định nào sau đây là đúng?
\(Q=\dfrac{x-3}{x^2}\).\(Q=x+3\).\(Q=\dfrac{x+3}{x}\).\(Q=-\dfrac{x+3}{x^2}\).Hướng dẫn giải:\(\dfrac{x^2+3x}{x-1}.Q=\dfrac{x^2-9}{x^2-x}\)
\(\Leftrightarrow Q=\dfrac{x^2-9}{x\left(x-1\right)}:\dfrac{x\left(x+3\right)}{x-1}\)
\(\Leftrightarrow Q=\dfrac{\left(x-3\right)\left(x+3\right)}{x\left(x-1\right)}.\dfrac{x-1}{x\left(x+3\right)}\)
\(\Leftrightarrow Q=\dfrac{x-3}{x^2}\).