Alignment of fractions of the form (a-b)/(c-d)

Question

The fraction \frac{num}{den} are usually rendered by centering the numerator and the denominator.

Unfortunately, I find the result in the following MWE quite ugly:

\documentclass{article}

\begin{document}

If $r\neq 1$, then 

\[
\sum_{k=0}^nr^k = \frac{1-r^{n+1}}{1-r}
\]

\end{document}

Indeed, the $r^{n+1}$ part is too big. I wish that the two - signs of a fraction of the form \frac{a-b}{c-d} to be vertically aligned (whatever the size of a,b,c and d) at the center of the fraction, in order to show the symmetry of the formula.

How can I get such a result?

Note: if it matters for the answer, I would like the alignment to work also for inline maths mode.

Answer 1

If you really think this is what you want, here's the \diffratio macro:

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand{\diffratio}[4]{%
  \frac
    {\diffratio@left{#1}{#3}-\diffratio@right{#2}{#4}}
    {\diffratio@left{#3}{#1}-\diffratio@right{#4}{#2}}%
}

\newcommand{\diffratio@left}[2]{%
  \mathpalette\diffratio@left@i{{#1}{#2}}%
}
\newcommand{\diffratio@right}[2]{%
  \mathpalette\diffratio@right@i{{#1}{#2}}%
}
\newcommand\diffratio@left@i[2]{%
  \diffratio@measure{#1}{#2}%
  \hb@xt@\dimen@{\hss\box\z@}%
}
\newcommand\diffratio@right@i[2]{%
  \diffratio@measure{#1}{#2}%
  \hb@xt@\dimen@{\box\z@\hss}%
}
\newcommand\diffratio@measure[2]{%
  \sbox\z@{$\m@th#1\@firstoftwo#2$}%
  \sbox\tw@{$\m@th#1\@secondoftwo#2$}%
  \dimen@=\wd\z@
  \ifdim\wd\tw@>\dimen@ \dimen@=\wd\tw@\fi
}
\makeatother

\begin{document}

\begin{gather*}
\diffratio{1}{x^{n+1}}{1}{x} \qquad \frac{1-x^{n+1}}{1-x} \\
\diffratio{a}{bc}{xy}{z} \qquad \frac{a-bc}{xy-z}
\end{gather*}

\end{document}

I have no doubt whatsoever that the normal \frac way is better.

Answer 2

Do you mean something like this?

That looks pretty ugly to me, but they say beauty is in the eye of the beholder ...

\documentclass{article}

\begin{document}

  If $r\neq 1$, then
  \[
  \sum_{k=0}^nr^k = \frac{1-r^{n+1}}{1-r^{\phantom{n+1}}}
  \]

\end{document}

Answer 3

If you really want the two to line up, you need to add \phantom as a space filler.

\documentclass{article}
\usepackage{mathtools}% for \mathrlap

\begin{document}

If $r\neq 1$, then 

\[
\sum_{k=0}^nr^k = \frac{1-r^{n+1}}{1-r^{\phantom{n+1}}}
 = \frac{1-r^{\mathrlap{n+1}}}{1-r} \phantom{\scriptstyle n+1}\textrm{with added white space}
\]

\end{document}