如何在编译之前打开/关闭整个文档的 \phantom

Question

我想创建一个包含大量公式和大量phantom空白的完形填空。但最终我需要两个版本，一个有空白，一个没有空白。手动删除所有phantom不是解决方案。有没有办法在编译时保留所有幻像命令但禁用幻像功能（针对整个文档）？换句话说，有没有办法为不同的编译打开/关闭幻像？

\documentclass{article}

\usepackage{amsmath}                    

\begin{document}

    \begin{align*}
        L(\lambda, x_1, x_2) &= U (x_1, x_2) - \lambda ( \phantom{p_1 x_1 + p_2 x_2 - m} ) \\
        \frac{\partial L}{\partial x_1} &= \frac{ \partial u}{\partial x_1} - \lambda p_1 \stackrel{!}{=} 0 \Rightarrow \phantom { \lambda = \frac{ 1}{p_1} \frac{ \partial u}{\partial x_1} } \tag{I} \\
        \frac{\partial L}{\partial x_2} &= \frac{ \partial u}{\partial x_2} - \lambda p_2 \stackrel{!}{=} 0 \Rightarrow \lambda = \frac{ 1}{p_2} \frac{ \partial u}{\partial x_2} \tag{II} \\
        \frac{\partial L }{\partial \lambda} &= - p_1 x_1 - p_2 x_2 + m \stackrel{!}{=} 0 \tag{III} \\
        \frac{ 1}{p_1} \frac{ \partial u}{\partial x_1} &= \frac{ 1}{p_2} \frac{ \partial u}{\partial x_2} \\
        \frac{ \frac{ \partial u}{\partial x_1}}{\frac{ \partial u}{\partial x_2}} &= \phantom { \frac{ p_1}{p_2}}
    \end{align*}


\end{document}