\(a,ĐK:x\ne0;x\ne-6\\ b,P=\dfrac{x^3+2x^2+2x^2-72+108-6x}{2x\left(x+6\right)}=\dfrac{x^3+4x^2-6x+36}{2x\left(x+6\right)}\\ P=\dfrac{x^3+6x^2-2x^2-12x+6x+36}{2x\left(x+6\right)}\\ P=\dfrac{\left(x+6\right)\left(x^2-2x+6\right)}{2x\left(x+6\right)}=\dfrac{x^2-2x+6}{2x}\\ c,P=\dfrac{3}{2}\Leftrightarrow6x=2x^2-4x+12\Leftrightarrow x^2-5x+6=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\left(tm\right)\\ d,P=-\dfrac{9}{2}\Leftrightarrow-18x=2x^2-4x+12\\ \Leftrightarrow x^2+7x+6=0\Leftrightarrow\left[{}\begin{matrix}x=-1\left(tm\right)\\x=-6\left(ktm\right)\end{matrix}\right.\)
\(e,P=1\Leftrightarrow x^2-2x+6=2x\Leftrightarrow x^2-4x+6=0\\ \Leftrightarrow\left(x-2\right)^2+2=0\Leftrightarrow\left(x-2\right)^2=-2\Leftrightarrow x\in\varnothing\)
