Cómo dividir ecuaciones largas con denominador largo en látex

Question

Soy nuevo en Latex, estoy intentando escribir la ecuación a continuación, pero tengo algunos errores, no pude encontrarlos.

 \documentclass{article}  
    \usepackage{amsmath}
    \begin{document}
    \begin{equation}
    \begin{split}
    E_q_2(A,B)
    &=\frac{1}{3n}\sum_{i=1}^{n}\frac{(1-e^{{-\mu}_A(x_i)})\times(1-e^{-\mu_B(x_i)})}{{(1-e^{{-\mu}_A(x_i)})}^2+{(1-e^{-\mu_B(x_i)})}^2-[(1-e^{{-\mu}_A(x_i)})\times(1-e^{-\mu_B(x_i)})]}\\
    &+ \frac{(1-e^{-(1-v_A(x_i))})\times(1-e^{-(1-v_B(x_i))})}{{(1-e^{-(1-v_A(x_i))})}^2+{(1-e^{-(1-v_B(x_i))})}^2-[(1-e^{-(1-v_A(x_i))})\times(1-e^{-(1-v_B(x_i))})]}\\
    &+\frac{(1-e^{-\frac{1}{2}(1+\mu_A(x_i)-v_A(x_i))})\times(1-e^{-\frac{1}{2}(1+\mu_B(x_i)-v_B(x_i))})}{
    \splitfrac{{(1-e^{-\frac{1}{2}(1+\mu_A(x_i)-v_A(x_i))})}^2+{(1-e^{-\frac{1}{2}(1+\mu_B(x_i)-v_B(x_i))})}^2 -}\\
     &{[(1-e^{-\frac{1}{2}(1+\mu_A(x_i)-v_A(x_i))})\times(1-e^{-\frac{1}{2}(1+\mu_B(x_i)-v_B(x_i))})]}}
    \end{split}
    \end{equation}
    \end{document}

Editado por @koleygr: (en orden de subíndices pero \splitfractambién eliminados)

MWE corregido:

\documentclass{article}  
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
E_{q_2}(A,B)
&=\frac{1}{3n}\sum_{i=1}^{n}\frac{(1-e^{{-\mu}_{A}(x_i)})\times(1-e^{-\mu_{B}(x_i)})}{{(1-e^{{-\mu}_{A}(x_i)})}^2+{(1-e^{-\mu_{B}(x_i)})}^2-[(1-e^{{-\mu}_{A}(x_i)})\times(1-e^{-\mu_{B}(x_i)})]}\\
&+ \frac{(1-e^{-(1-v_{A}(x_i))})\times(1-e^{-(1-v_{B}(x_i))})}{{(1-e^{-(1-v_{A}(x_i))})}^2+{(1-e^{-(1-v_{B}(x_i))})}^2-[(1-e^{-(1-v_{A}(x_i))})\times(1-e^{-(1-v_{B}(x_i))})]}\\
&+\frac{(1-e^{-\frac{1}{2}(1+\mu_{A}(x_i)-v_{A}(x_i))})\times(1-e^{-\frac{1}{2}(1+\mu_{B}(x_i)-v_{B}(x_i))})}{
{(1-e^{-\frac{1}{2}(1+\mu_{A}(x_i)-v_{A}(x_i))})}^2+{(1-e^{-\frac{1}{2}(1+\mu_{B}(x_i)-v_{B}(x_i))})}^2 -[(1-e^{-\frac{1}{2}(1+\mu_{A}(x_i)-v_{A}(x_i))})\times(1-e^{-\frac{1}{2}(1+\mu_{B}(x_i)-v_{B}(x_i))})]}
\end{split}
\end{equation}
\end{document}

Answer 1

Si lo estuviera escribiendo, usaría algo como

\documentclass{article}  
\usepackage{mathtools}
\begin{document}
\begin{equation}
E_{q_2}(A,B) = \frac{1}{3n}\sum_{i=1}^{n} \left( \frac{P_1(x_i)}{Q_1(x_i)}
    + \frac{P_2(x_i)}{Q_2(x_i)} + \frac{P_3(x_i)}{Q_3(x_i)} \right)
\end{equation}
where 
\addtocounter{equation}{-1}%
\begin{subequations}
\begin{align}
P_1(x_i) &= \left(1-e^{{-\mu}_{A}(x_i)}\right)\left(1-e^{-\mu_{B}(x_i)}\right)\\
Q_1(x_i) &= \left(1-e^{{-\mu}_{A}(x_i)}\right)^2+\left(1-e^{-\mu_{B}(x_i)}\right)^2 \notag\\
  &\quad - \left(1-e^{{-\mu}_{A}(x_i)}\right)\left(1-e^{-\mu_{B}(x_i)}\right)\\
P_2(x_i) &= \left(1-e^{-(1-v_{A}(x_i))}\right)\left(1-e^{-(1-v_{B}(x_i))}\right)\\
Q_2(x_i) &= \left(1-e^{-(1-v_{A}(x_i))}\right)^2+\left(1-e^{-(1-v_{B}(x_i))}\right)^2 \notag\\
  &\quad - \left(1-e^{-(1-v_{A}(x_i))}\right)\left(1-e^{-(1-v_{B}(x_i))}\right)\\
P_3(x_i) &= \left(1-e^{-\frac{1}{2}(1+\mu_{A}(x_i)-v_{A}(x_i))}\right)
    \left(1-e^{-\frac{1}{2}(1+\mu_{B}(x_i)-v_{B}(x_i))}\right)\\
\shortintertext{and}
Q_3(x_i) &= \left(1-e^{-\frac{1}{2}(1+\mu_{A}(x_i)-v_{A}(x_i))}\right)^2
    +\left(1-e^{-\frac{1}{2}(1+\mu_{B}(x_i)-v_{B}(x_i))}\right)^2 \notag\\
  &\quad - \left(1-e^{-\frac{1}{2}(1+\mu_{A}(x_i)-v_{A}(x_i))}\right)
    \left(1-e^{-\frac{1}{2}(1+\mu_{B}(x_i)-v_{B}(x_i))}\right)
\end{align}
\end{subequations}

\end{document}

Answer 2

(Esta respuesta se basa en el código proporcionado en el "MWE corregido" anterior).

Te sugiero que cargues el mathtoolspaquete y uses varias \splitdfracinstrucciones \splitfrac; Vea a continuación una aplicación de esta idea. En segundo lugar, reemplazaría la e^{...}notación con \exp(...), ya que de lo contrario no sería fácil leer el material en superíndice de segundo nivel. En tercer lugar, usaría \bigly \bigrpara aumentar el tamaño de algunos (pero ciertamente no todos) paréntesis y corchetes.

\documentclass{article}  
\usepackage{mathtools} % for '\splitfrac' macro
\DeclareMathOperator{\E}{E} % expectations operator
\begin{document}
\begin{align}
\E_{q_2}(A,B)
&=\frac{1}{3n}\sum_{i=1}^{n}
\frac{\bigl[1-\exp\bigl(-\mu_{\!A}(x_i)\bigr)\bigr]\times
      \bigl[1-\exp\bigl(-\mu_{\!B}(x_i)\bigr)\bigr]}{%
 \biggl(\splitdfrac{%
 \bigl[1-\exp\bigl(-\mu_{\!A}(x_i)\bigr)\bigr]^2
+\bigl[1-\exp\bigl(-\mu_{\!B}(x_i)\bigr)\bigr]^2}{%
-\bigl[1-\exp\bigl(-\mu_{\!A}(x_i)\bigr)\bigr]\times
       \bigl[1-\exp\bigl(-\mu_{\!B}(x_i)\bigr)\bigr]}
 \biggr)} \notag\\[1ex]
&+\frac{\bigl[1-\exp\bigl(-(1-v_{\!A}(x_i))\bigr)\bigr]\times
        \bigl[1-\exp\bigl(-(1-v_{\!B}(x_i))\bigr)\bigr]}{%
 \biggl(\splitdfrac{%
  \bigl[1-\exp\bigl(-(1-v_{\!A}(x_i))\bigr)\bigr]^2
 +\bigl[1-\exp\bigl(-(1-v_{\!B}(x_i))\bigr)\bigr]^2}{%
 -\bigl[1-\exp\bigl(-(1-v_{\!A}(x_i))\bigr)\bigr]\times
         \bigl[1-\exp\bigl(-(1-v_{\!B}(x_i))\bigr)\bigr]}
 \biggr)} \notag\\[1ex]
&+\frac{%
 \biggl(\splitdfrac{%
   \bigl[1-\exp\bigl(-\frac{1}{2}(1+\mu_{\!A}(x_i)-v_{\!A}(x_i))\bigr)\bigr]}{%
   \times
   \bigl[1-\exp\bigl(-\frac{1}{2}(1+\mu_{\!B}(x_i)-v_{\!B}(x_i))\bigr)\bigr]}
 \biggr)}{%
 \left(\splitdfrac{%
   \splitfrac{%
   \bigl[1-\exp\bigl(-\frac{1}{2}(1+\mu_{\!A}(x_i)-v_{\!A}(x_i))\bigr)\bigr]^2}{%
  +\bigl[1-\exp\bigl(-\frac{1}{2}(1+\mu_{\!B}(x_i)-v_{\!B}(x_i))\bigr)\bigr]^2}}{% 
   \splitfrac{%
   {}-{} % make this a binary rather than a unary operator... 
    \bigl[1-\exp\bigl(-\frac{1}{2}(1+\mu_{\!A}(x_i)-v_{\!A}(x_i))\bigr)\bigr]}{
    \times
    \bigl[1-\exp\bigl(-\frac{1}{2}(1+\mu_{\!B}(x_i)-v_{\!B}(x_i))\bigr)\bigr]}}
 \right)}
\end{align}
\end{document}

Answer 3

He editado el código de @mico para hacerlo un poco más corto.

\documentclass{article}  
\usepackage{mathtools} % for '\splitfrac' macro
\DeclareMathOperator{\E}{E} % expectations operator
\DeclarePairedDelimiter{\parens}()
\DeclarePairedDelimiter{\sparens}[]

\newcommand{\myexp}[1]{\exp\parens[\big]{#1}}
\newcommand{\ome}[1]{\sparens[\big]{1-\myexp{#1}}}

\begin{document}
\begin{align}
\E_{q_2}(A,B)
&=\frac{1}{3n}\sum_{i=1}^{n}
\frac{\ome{-\mu_{\!A}(x_i)}\times
      \ome{-\mu_{\!B}(x_i)}}{%
 \biggl(\splitdfrac{%
 \ome{-\mu_{\!A}(x_i)}^2
+\ome{-\mu_{\!B}(x_i)}^2}{%
-\ome{-\mu_{\!A}(x_i)}\times
       \ome{-\mu_{\!B}(x_i)}}\biggr)} \notag\\[1ex]
&+\frac{\ome{-(1-v_{\!A}(x_i))}\times
        \ome{-(1-v_{\!B}(x_i))}}{%
 \biggl(\splitdfrac{%
  \ome{-(1-v_{\!A}(x_i))}^2
 +\ome{-(1-v_{\!B}(x_i)))}^2}{%
 -\bigl\{\ome{-(1-v_{\!A}(x_i))}\times
         \ome{-(1-v_{\!B}(x_i))}\bigr\}}
 \biggr)} \notag\\[1ex]
&+\frac{%
 \biggl(\splitdfrac{%
   \ome{-\frac{1}{2}(1+\mu_{\!A}(x_i)-v_{\!A}(x_i))}}{%
   \times
   \ome{-\frac{1}{2}(1+\mu_{\!B}(x_i)-v_{\!B}(x_i))}}
 \biggr)}{%
 \left(\splitdfrac{%
   \splitfrac{%
   \ome{-\frac{1}{2}(1+\mu_{\!A}(x_i)-v_{\!A}(x_i))}^2}{%
  +\ome{-\frac{1}{2}(1+\mu_{\!B}(x_i)-v_{\!B}(x_i))}^2}}{% 
   \splitfrac{%
   -\ome{-\frac{1}{2}(1+\mu_{\!A}(x_i)-v_{\!A}(x_i))}}{
    \times
    \ome{-\frac{1}{2}(1+\mu_{\!B}(x_i)-v_{\!B}(x_i))}\bigr\} }}
 \right)}
\end{align}
\end{document}

Y, con márgenes más pequeños, el código se puede desinfectar aún más:

\documentclass{article}  
\usepackage[margin=1in]{geometry}
\usepackage{mathtools} % for '\splitfrac' macro
\DeclareMathOperator{\E}{E} % expectations operator
\DeclarePairedDelimiter{\parens}()
\DeclarePairedDelimiter{\sparens}[]

\newcommand{\myexp}[1]{\exp\parens[\big]{#1}}
\newcommand{\ome}[1]{\sparens[\big]{1-\myexp{#1}}}

\newcommand{\rat}[2]{%
\frac{\ome{#1} \times \ome{#2}}{
\parens[\bigg]{\splitdfrac{\ome{#1}^2 + \ome{#2}^2}{- \ome{#1}\times \ome{#2}}}}
}


\begin{document}
\begin{multline}
\E_{q_2}(A,B)
=\frac{1}{3n}\sum_{i=1}^{n}
\rat{-\mu_{\!A}(x_i)}{-\mu_{\!B}(x_i)}
\\
+\rat{-(1-v_{\!A}(x_i))}{-(1-v_{\!B}(x_i))}\\
+
 \rat{-\frac{1}{2}(1+\mu_{\!A}(x_i)-v_{\!A}(x_i))}{%
   {-\frac{1}{2}(1+\mu_{\!B}(x_i)-v_{\!B}(x_i))}}.
\end{multline}
\end{document}