a) M xác định \(\Leftrightarrow4x^3-9x\ne0\)
\(\Leftrightarrow x\left(4x^2-9\right)\ne0\\ \Leftrightarrow\left[{}\begin{matrix}x\ne0\\x\ne\pm\dfrac{3}{2}\end{matrix}\right.\)
b)
\(M=\dfrac{\left(2x^3+3x^2\right)\left(2x+1\right)}{4x^3-9x}=\dfrac{4x^4+2x^3+6x^3+3x^2}{4x^3-9x}\\ =\dfrac{4x^4+8x^3+3x^2}{4x^3-9x}\\ =\dfrac{x\left(4x^3+8x^2+3x\right)}{x\left(x^2-9\right)}\\ =\dfrac{4x^3+8x^2+3x}{x^2-9}\)
c)
\(M=0\\ \Leftrightarrow\left(2x^3+3x^2\right)\left(2x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x^3+3x^2=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2\left(2x+3\right)=0\\x=-\dfrac{1}{2}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{3}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
