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The following code generates

\begin{align}
    S_{12} =\frac{S_{1,21}\, S_{2,21}}{2\, S_{1,22}\, S_{2,22}\, C_{12}} \left(\sqrt{\frac{\begin{aligned}
                {S_{1,21}}^2\, {S_{2,21}}^2 - S_{1,11}\, S_{1,22}\, {S_{2,21}}^2 - {S_{1,21}}^2\, S_{2,11}\, S_{2,22}\\
                + S_{1,22}\, {S_{2,21}}^2\, C_{11} + 4\, S_{1,22}\, S_{2,22}\, {C_{12}}^2 + {S_{1,21}}^2\, S_{2,22}\, C_{22}\\
                + S_{1,11}\, S_{1,22}\, S_{2,11}\, S_{2,22} - S_{1,11}\, S_{1,22}\, S_{2,22}\, C_{22}\\
                - S_{1,22}\, S_{2,11}\, S_{2,22}\, C_{11} + S_{1,22}\, S_{2,22}\, C_{11}\, C_{22}
                \end{aligned}}{\begin{aligned}
                \left({S_{1,21}}^2 + S_{1,22}\, C_{11} - S_{1,11}\, S_{1,22}\right)\, \left({S_{2,21}}^2 + S_{2,22}\, C_{22} - S_{2,11}\, S_{2,22}\right)
                \end{aligned}}} - 1 \right)
    \end{align}

enter image description here

How to get rid of blank space in the lower area of the brackets?

2

1 Answer 1

1

Here's my suggestion: split the formulas. Find better names instead of $A$ and $B$.

\documentclass{article}
\usepackage{newtxtext,newtxmath}
\usepackage{amsmath}

\begin{document}

\begin{equation}
S_{12} =
\frac{S_{1,21} S_{2,21}}{2 S_{1,22} S_{2,22} C_{12}}
\left(\sqrt{\frac{A}{B}} - 1 \right)
\end{equation}
where
\begin{equation*}
\begin{aligned}
A &=
  {S_{1,21}}^2 {S_{2,21}}^2 - S_{1,11} S_{1,22} {S_{2,21}}^2 - {S_{1,21}}^2 S_{2,11} S_{2,22}\\
  &\quad+
  S_{1,22} {S_{2,21}}^2 C_{11} + 4 S_{1,22} S_{2,22} {C_{12}}^2 + {S_{1,21}}^2 S_{2,22} C_{22}\\
  &\quad+
  S_{1,11} S_{1,22} S_{2,11} S_{2,22} - S_{1,11} S_{1,22} S_{2,22} C_{22}\\
  &\quad-
  S_{1,22} S_{2,11} S_{2,22} C_{11} + S_{1,22} S_{2,22} C_{11} C_{22} \\[1ex]
B &=
  ({S_{1,21}}^2 + S_{1,22} C_{11} - S_{1,11} S_{1,22})
  ({S_{2,21}}^2 + S_{2,22} C_{22} - S_{2,11} S_{2,22})
\end{aligned}
\end{equation*}

\end{document}

enter image description here

I also suggest

S_{1,21}^2

instead of {S_{1,21}}^2 that makes the exponent hanging from nowhere.

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