Cho biết phân thức P thỏa mãn \(\dfrac{2x^2+x-6}{P}=\dfrac{2x-3}{x+2}\). Khẳng định nào sau đây là đúng?
\(P=\left(x+2\right)\left(x-2\right)\).\(P=-\left(x+2\right)\left(x-2\right)\).\(P=2x^2-2x\).\(P=3x^2+1\).Hướng dẫn giải:\(\dfrac{2x^2+x-6}{P}=\dfrac{2x-3}{x+2}\)
\(\Leftrightarrow\dfrac{\left(x+2\right)\left(2x-3\right)}{P}=\dfrac{2x-3}{x-2}\)
\(\Leftrightarrow P\left(2x-3\right)=\left(x+2\right)\left(x-2\right)\left(2x-3\right)\)
\(\Leftrightarrow P=\left(x+2\right)\left(x-2\right)\left(2x-3\right):\left(2x-3\right)\)
\(\Leftrightarrow P=\left(x+2\right)\left(x-2\right)\).
