How should I represent the conjugate of a term in the denominator?

Question

Using \overline for a term in the denominator creates a cluttered look, and \Bar results in a really faint line. Also I only know how to use \Bar over one letter at a time.

\documentclass{article}
\usepackage{amsmath,amsfonts,mathtools}

\begin{document}
\begin{align*}
\frac{z_0 - z_1}{\overline{z_0 - z_1}} +
\frac{z_0 - z_1}{\Bar{z}_0 - \Bar{z}_1}
\end{align*}
\end{document}

I want to have a line that doesn't clash with the fraction line, but that also doesn't require squinting to observe. What are your recommendations? My best idea right now is to color the line gray, but I don't how to do that.

Edit: Actually, a thin line over the whole term, similar to the one produced by \Bar, might just work.

Answer 1

How about this?

\documentclass{article}
\usepackage{amsfonts,mathtools}
\newcommand{\conjug}[1]{{\fontdimen8\textfont3=0.25pt\mkern2mu\overline{\mkern-1mu #1\mkern-2mu}}\mkern2mu}

\begin{document}

\begin{align*}
\frac{z_0 - z_1}{\conjug{z_0 - z_1}} + \frac{z_0 - z_1}{\Bar{z}_0 - \Bar{z}_1}
\end{align*}

\end{document}