[Tex/LaTex] Alignment of fractions of the form (a-b)/(c-d)

fractionshorizontal alignment

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.

Best Answer

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.

Fractions

I'd just use the normal \frac or \tfrac. For display style maths they still look the best. I would use \nicefrac (or similar) only (if at all) in text maths.

Code

\documentclass{article}
\usepackage{amsmath}
\def\frstfrac{\frac{2}{\sqrt{2y+1}\sqrt{2 \pi}}} % just a shortcut
\begin{document}
\begin{align*}
  &= \frstfrac       \exp \left(            -y - \frac{1}{2}\right)  && \forall y \in  \left[- \frac{1}{2}, \infty\right) \\
  &= \frstfrac \cdot  e^{                   -y - \frac{1}{2}}        && \forall y \in  \left[-\tfrac{1}{2}, \infty\right) \\
  &= \frstfrac \cdot  e^{           -  \left(y + \frac{1}{2}\right)} && \forall y \in  \left[-\tfrac{1}{2}, \infty\right) \\
  &= \frstfrac \cdot  e^{\textstyle -\!\left(y + \frac{1}{2}\right)} && \forall y \in  \left[-\tfrac{1}{2}, \infty\right) \\
  &= \frstfrac       \exp \left(            -y - 1/2 \right)         && \forall y \in  \left[-       1/ 2 , \infty\right)
\end{align*}
\end{document}

Output

$different outputs of the fraction$

`\smash`

Also, consider using \sqrt{\smash[b]{2y+1}}\sqrt{\smash[b]{2 \pi}} in your denominator for better roots.

To quote from the amsmath documentation:

With the amsmath package \smash has optional arguments t and b, because occasionally it is advantageous to be able to “smash” only the top or only the bottom of something while retaining the natural depth or height.

Compare:

Code

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
  \frac{2}{\sqrt{\smash[b]{2y+1}}\sqrt{\smash[b]{2 \pi}}} = \frac{2}{\sqrt{2y+1}\sqrt{2 \pi}}
\end{equation*}
\end{document}

Output

smash example

The top bar of the root is aligned different and even the lower point is not on equal heights.

LaTeX Companion

The LaTeX Companion has a very elaborated text about \smash and its uses. The first two examples (licensed under the LPPL) are shown here. Take a close look at the root's lower end and the top bar.

Code

\documentclass{article}
\usepackage{amsmath}
\begin{document}

$ \sqrt{x} + \sqrt{y}            + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\mathstrut y} + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\smash{y}}    + \sqrt{z} $ \par
$ \sqrt{x} + \sqrt{\smash[b]{y}} + \sqrt{z} $

\[
   \sqrt{ \frac{a+b}{         x_j   } } \quad
   \sqrt{ \frac{a+b}{  \smash{x_j  }} } \quad
   \sqrt{ \frac{a+b}{{}\smash{x_j  }} } \quad
   \sqrt{ \frac{a+b}{  \smash{x_j+b}} }
\]
\end{document}

Output

square root example $fraction example$

[Tex/LaTex] Continued fractions

The following code is "full" LaTeX:

\documentclass{article}
\usepackage{amsmath} % for "\cfrac" macro
\begin{document}
\[
e=2+\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{ 1+\cfrac{1}{1+\cfrac{1}{4+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{6+\cdots}}}}}}}}
\]
\end{document}

If you want, you can copy and paste the math part -- the stuff between \[ and \] -- into latex2png.com.

Best Answer

Related Solutions

[Tex/LaTex] issues with fractions

Fractions

Code

Output

\smash

Code

Output

LaTeX Companion

Code

Output

[Tex/LaTex] Continued fractions

Related Question

`\smash`