Cómo dividir ecuaciones largas con denominador largo en látex

Solución:

(esta respuesta se basa en el código proporcionado en el “MWE corregido” anterior).

Te sugiero que cargues el mathtools empaquetar y usar varios splitdfrac y splitfrac instrucciones; vea a continuación una aplicación de esta idea. En segundo lugar, reemplazaría el e^{...} notación con exp(...), ya que de lo contrario no es fácil leer el material de superíndice de segundo nivel. Tercero, usaría bigl y bigr para aumentar el tamaño de algunos (pero ciertamente no todos) paréntesis y corchetes redondos.

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-expbigl(-mu_{!A}(x_i)bigr)bigr]times
      bigl[1-expbigl(-mu_{!B}(x_i)bigr)bigr]}{%
 biggl(splitdfrac{%
 bigl[1-expbigl(-mu_{!A}(x_i)bigr)bigr]^2
+bigl[1-expbigl(-mu_{!B}(x_i)bigr)bigr]^2}{%
-bigl[1-expbigl(-mu_{!A}(x_i)bigr)bigr]times
       bigl[1-expbigl(-mu_{!B}(x_i)bigr)bigr]}
 biggr)} notag\[1ex]
&+frac{bigl[1-expbigl(-(1-v_{!A}(x_i))bigr)bigr]times
        bigl[1-expbigl(-(1-v_{!B}(x_i))bigr)bigr]}{%
 biggl(splitdfrac{%
  bigl[1-expbigl(-(1-v_{!A}(x_i))bigr)bigr]^2
 +bigl[1-expbigl(-(1-v_{!B}(x_i))bigr)bigr]^2}{%
 -bigl[1-expbigl(-(1-v_{!A}(x_i))bigr)bigr]times
         bigl[1-expbigl(-(1-v_{!B}(x_i))bigr)bigr]}
 biggr)} notag\[1ex]
&+frac{%
 biggl(splitdfrac{%
   bigl[1-expbigl(-frac{1}{2}(1+mu_{!A}(x_i)-v_{!A}(x_i))bigr)bigr]}{%
   times
   bigl[1-expbigl(-frac{1}{2}(1+mu_{!B}(x_i)-v_{!B}(x_i))bigr)bigr]}
 biggr)}{%
 left(splitdfrac{%
   splitfrac{%
   bigl[1-expbigl(-frac{1}{2}(1+mu_{!A}(x_i)-v_{!A}(x_i))bigr)bigr]^2}{%
  +bigl[1-expbigl(-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-expbigl(-frac{1}{2}(1+mu_{!A}(x_i)-v_{!A}(x_i))bigr)bigr]}{
    times
    bigl[1-expbigl(-frac{1}{2}(1+mu_{!B}(x_i)-v_{!B}(x_i))bigr)bigr]}}
 right)}
end{align}
end{document}

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}

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]{expparens[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]{expparens[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}

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