如何以理想的方式写出长分数表达式？

Question

考虑以下 MWE：

\documentclass[12pt, a4paper]{report}
\usepackage{amsfonts, graphicx, verbatim, mathtools,amssymb, amsthm, mathrsfs,amsmath}
\begin{document}
\begin{align}
S_2^* &= \frac{(\gamma_A + \sigma+\mu)(\gamma_I+\eta+\alpha+\mu)}{\beta_A(\gamma_I+\eta+\alpha+\mu)+\sigma \beta_I}\\[1ex]
A_2^* &= \frac{\gamma_I+\eta+\alpha+\mu}{\sigma}I_2^*\\[1ex]
I_2^* &= \frac{\mu  \sigma  (\gamma_A+\mu +\sigma ) (\mu +\xi +\rho ) (\alpha +\gamma_I+\eta +\mu )}{\beta_A (\alpha +\gamma_I+\eta +\mu )+\beta_I \sigma ) (\mu  (\gamma_A+\mu +\xi ) (\alpha +\gamma_I+\eta +\mu )+\alpha  \sigma  (\mu +\xi )+\mu  \sigma  (\gamma_I+\eta +\mu +\xi ))}(\mathcal{R}_0 -1)\\[1ex]
R_2^* &= \frac{\gamma_A(\gamma_I + \eta+\alpha+\nu)I_2^*+\sigma(I_2^*(\gamma_I+\eta)+b\nu+\rho S_2^*)}{\sigma(\mu+\rho)}
\end{align}
\end{document}

我们发现 $I_2^*$ 的表达式不适合该页面，那么解决这个问题的理想方法是什么？

Answer 1

您可以使用matrix环境将方程 (3) 中非常长的分母项分成三行。

\documentclass[12pt, a4paper]{report}
\usepackage{amsmath,amssymb} % I've simplified the preamble as much as possible
\begin{document}
\begingroup % localize scope of next instruction:
\addtolength\jot{1ex} % increase spacing beween rows
\begin{align}
S_2^* &= \frac{(\gamma_A + \sigma+\mu)(\gamma_I+\eta+\alpha+\mu)}{\beta_A(\gamma_I+\eta+\alpha+\mu)+\sigma \beta_I}\\
A_2^* &= \frac{\gamma_I+\eta+\alpha+\mu}{\sigma}I_2^*\\
I_2^* &= \frac{\mu  \sigma  (\gamma_A+\mu +\sigma) (\mu +\xi +\rho) (\alpha +\gamma_I+\eta +\mu)}{%
   \left(%
   \begin{matrix}
   \beta_A (\alpha +\gamma_I+\eta +\mu) \hfill \\
   {}+\beta_I \sigma  \bigl[\mu  (\gamma_A+\mu +\xi) (\alpha +\gamma_I+\eta +\mu)\\
   \hfill {}+\alpha  \sigma  (\mu +\xi)+\mu  \sigma  (\gamma_I+\eta +\mu +\xi)\bigr]
   \end{matrix}
   \right)}(\mathcal{R}_0 -1)\\ 
R_2^* &= \frac{\gamma_A(\gamma_I + \eta+\alpha+\nu)I_2^*
    +\sigma[I_2^*(\gamma_I+\eta)+b\nu+\rho S_2^*]}{\sigma(\mu+\rho)}
\end{align}
\endgroup
\end{document}

Answer 2

这是一种将变量分别分配给分子和分母，然后写$I_2^*$为它们的比率的方法。

\documentclass[12pt, a4paper]{report}
\usepackage{amsmath}
\begin{document}
\begin{align}
S_2^* &= \frac{(\gamma_A + \sigma+\mu)(\gamma_I+\eta+\alpha+\mu)}{\beta_A(\gamma_I+\eta+\alpha+\mu)+\sigma \beta_I}\\[1ex]
A_2^* &= \frac{\gamma_I+\eta+\alpha+\mu}{\sigma}I_2^*\\[1ex]
I_{2,1}^* &= \mu  \sigma  (\gamma_A+\mu +\sigma ) (\mu +\xi +\rho ) (\alpha +\gamma_I+\eta +\mu )\\
I_{2,2}^* &= \beta_A (\alpha +\gamma_I+\eta +\mu )+\beta_I \sigma (\mu  (\gamma_A+\mu +\xi ) (\alpha +\gamma_I+\eta +\mu )\nonumber\\
          &\quad +\alpha  \sigma  (\mu +\xi )+\mu  \sigma  (\gamma_I+\eta +\mu +\xi )) \\
I_2^* &= \frac{I_{2,1}^*}{I_{2,2}^*}(\mathcal{R}_0 -1)\\[1ex]
R_2^* &= \frac{\gamma_A(\gamma_I + \eta+\alpha+\nu)I_2^*+\sigma(I_2^*(\gamma_I+\eta)+b\nu+\rho S_2^*)}{\sigma(\mu+\rho)}
\end{align}
\end{document}

Answer 3

我将定义一个辅助变量，设为，A = \gamma_I + \eta + \alpha + \mu并将您的方程写为：

\documentclass[12pt, a4paper]{report}
\usepackage{mathtools, amssymb, amsthm, mathrsfs}

\begin{document}
Let be $A$ defined as
\begin{spreadlines}{2ex}
\begin{align}
A & = \gamma_I + \eta + \alpha + \mu
\shortintertext{and}
S_2^* 
    & = \frac{(\gamma_A + \sigma + \mu)A}{\beta_A A + \sigma \beta_I}   \\
I_2^* &= \frac{\mu \sigma (\gamma_A + \mu + \sigma )(\mu + \xi + \rho)A(\mathcal{R}_0 -1)}
              {(\beta_A A + \beta_I\sigma)(\mu(\gamma_A+\mu +\xi)A + \alpha\sigma(\mu +\xi )+\mu \sigma (\gamma_I+\eta +\mu +\xi))}                  \\
\intertext{then}
A_2^*
    & = \frac{A}{\sigma}I_2^*                                           \\
R_2^*
    & = \frac{\gamma_A(\gamma_I + \eta+\alpha+\nu)I_2^* + \sigma(I_2^*(\gamma_I+\eta)+b\nu+\rho S_2^*)}{\sigma(\mu+\rho)}
\end{align}
\end{spreadlines}
\end{document}

Answer 4

我将以这种方式使用\splitfrac命令mathtools（以加载amsmath）：

    \documentclass[12pt, a4paper]{report}
    \usepackage{graphicx, verbatim, mathtools,amssymb, amsthm, mathrsfs,mathtools}
    \usepackage{showframe}

    \begin{document}

    \begin{align}
    S_2^* &= \frac{(\gamma_A + \sigma+\mu)(\gamma_I+\eta+\alpha+\mu)}{\beta_A(\gamma_I+\eta+\alpha+\mu)+\sigma \beta_I}\\[1ex]
    A_2^* &= \frac{\gamma_I+\eta+\alpha+\mu}{\sigma}I_2^*\\[1ex]
    I_2^* &= \frac{\mu \sigma (\gamma_A+\mu +\sigma ) (\mu +\xi +\rho ) (\alpha +\gamma_I+\eta +\mu )(\mathcal{R}_0 -1)}{\splitfrac{\beta_A (\alpha +\gamma_I+\eta +\mu )+\beta_I \sigma ) (\mu (\gamma_A+\mu +\xi ) (\alpha +\gamma_I+\eta +\mu )}{+\alpha \sigma (\mu +\xi )+\mu \sigma (\gamma_I+\eta +\mu +\xi ))}}\\[1ex]
    R_2^* &= \frac{\gamma_A(\gamma_I + \eta+\alpha+\nu)I_2^*+\sigma(I_2^*(\gamma_I+\eta)+b\nu+\rho S_2^*)}{\sigma(\mu+\rho)}
    \end{align}

    \end{document} 

无关amsfonts：加载时无需加载amssymb– 后者会为您完成加载。