$a)$

$\{\begin{array}{l}4x\ne 0\\ x^2\ne 0\end{array}\Rightarrow \{\begin{array}{l}x\ne 0\\ x\ne 0\end{array}\Rightarrow D=\mathbb{R}\backslash \left\{0\right\}$

$\frac{1}{4x}+\frac{2}{x^2}=\frac{x^2}{4x\cdot x^2}+\frac{2\cdot 4x}{x^2\cdot 4x}=\frac{x^2}{4x^3}+\frac{8x}{4x^3}=\frac{x^2+8x}{4x^3}$