# How to reduce unnecessary space in the brackets under the equation?

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}


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

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

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

\begin{document}

$$S_{12} = \frac{S_{1,21} S_{2,21}}{2 S_{1,22} S_{2,22} C_{12}} \left(\sqrt{\frac{A}{B}} - 1 \right)$$
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}\\
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} \\[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}


I also suggest

S_{1,21}^2


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