Separate Fraction or not in Equation

Question

I want to write the equation for hyperbolic sinh in my document. But I can't find a way which I think looks good. The alternatives I have tried are:

\begin{equation} \label{sinh_eq}
\frac{1}{2}\Bigl(e^{Y_{d,h}}-e^{Y_{d,h}}\Bigr)
\end{equation}

and:

\begin{equation} \label{sinhx_eq}
\frac{e^{Y_{d,h}}-e^{Y_{d,h}}}{2}.
\end{equation}

I have been taught that the first alternative is the right way to write this type of equation, but I think it looks quite bad (1/2 looks too big). The second one looks better imo, but is this a correct way of writing it? For other similar equations in my document I use the first alternative so it would be nice to have the same style.

The equations can be visualized here and here.

I am also attaching pictures below.

Answer 1

Do alternatives 3 and/or 4 in the following screenshot look better to you than first two alternatives?

\documentclass{article} % or some other suitable document class
\usepackage{amsmath} % for 'align*' env.
\usepackage{newpxtext,newpxmath} % optional (Palatino clone text and math fonts)

\begin{document}

\begin{align*}
\sinh (Y_{d,h})
&= \frac{1}{2} \bigl(e^{Y_{d,h}}-e^{-Y_{d,h}}\bigr) \\ 
&= \frac{e^{Y_{d,h}}-e^{-Y_{d,h}}}{2}  \\
&= \bigl(e^{Y_{d,h}}-e^{-Y_{d,h}}\bigr)\big/2 \\
&= \tfrac{1}{2} \bigl(\exp(Y_{d,h})-\exp(-Y_{d,h})\bigr) 
\end{align*}

\end{document}

Answer 2

I would not use the over-sized parentheses, but any of these seem OK, depending on your preferences

\documentclass{article}

\usepackage{amsmath}

\begin{document}

frac 1 2
\begin{equation}
\frac{1}{2}(e^{Y_{d,h}}-e^{Y_{d,h}})
\end{equation}

tfac 1 2
\begin{equation}
\tfrac{1}{2}(e^{Y_{d,h}}-e^{Y_{d,h}})
\end{equation}

frac
\begin{equation}
\frac{e^{Y_{d,h}}-e^{Y_{d,h}}}{2}
\end{equation}

/
\begin{equation}
(e^{Y_{d,h}}-e^{Y_{d,h}})/2
\end{equation}

\end{document}