Huge white space in fraction

Question

I'm trying to create an equation in LaTeX, however, there seems to be a gigantic white space that is rather unsightly. Here's the code I'm using:

\[
x=a\sqrt[n]{1-\left(\dfrac{\sqrt[n]{\dfrac{\sqrt[2-n]{\left(\dfrac{a} 
{b}\right)^{2n}}}{\dfrac{1}{a^n}+\dfrac{1}{b^n}\left(\sqrt[2-n] 
{\left(\dfrac{a}{b}\right)^{2n}}\right)}}}{b}\right)^n}
\]

Is there a way to shorten the braces and root so that they look somewhat closer to this?

The short answer is that it is the parentheses that are the problem, not the fraction per se: For TeX likes to make parenteses symmetrical about the math axis, which in this case is the main fraction bar. (I think I saw an answer to a related question recently that dealt with this. I'll see if I can manage to find it again …) — Harald Hanche-Olsen, Oct 24 '18 at 18:43
Ah, found it. This answer deals with a somewhat similar problem. You might have a look and see if you can adapt it to your situation. (Or if not, perhaps someone else reading this can step in and help out.) — Harald Hanche-Olsen, Oct 24 '18 at 18:53
moving the parenthesis of the math axis makes rather ugly output, can you not use \left(\frac{1}{b}\sqrt{.....}\right) — David Carlisle, Oct 24 '18 at 20:18
Related: How do I fix the vertical alignment of the bracketed part of this equation?, Is there a way to modify the default vertical spacing conventions of LaTeX left and right delimiters? — Werner, Oct 24 '18 at 20:33

score 2 · Answer 1 · answered Oct 24 '18 at 20:55

I'm not sure such a horrible formula can help the reader.

Anyway it's possible to make it less ugly without guessing dimensions. I added a two-story version, anyhow.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
\sbox0{$\displaystyle
  \dfrac{
    \sqrt[n]{
      \dfrac{
        \sqrt[2-n]{\left(\dfrac{a}{b}\right)^{2n}}
      }{
        \dfrac{1}{a^n}+
        \dfrac{1}{b^n}\sqrt[2-n]{\left(\dfrac{a}{b}\right)^{2n}}
      }
    }
  }{b}
$}
%
x=a\sqrt[n]{
  1-
  \raisebox{\dimexpr\depth-3\fontdimen22\textfont2}{$
    \left(\begin{gathered}\usebox{0}\end{gathered}\:\right)^n
  $}
}
\]

\[
x=a
\left(1-
  \left(
    \dfrac{1}{b}
    \sqrt[n]{
      \dfrac{
        (a/b)^{2n/(2-n)}
      }{
        a^{-n}+b^{-n}(a/b)^{2n/(2-n)}
      }
    }\,
  \right)^{\!\!n}\;
\right)^{\!\!1/n}
\]

\end{document}

score 0 · Answer 2 · answered Oct 24 '18 at 20:19

I propose this hack, found with trial and error:

\documentclass{article}
 \usepackage{mathtools}

\begin{document}

\[
\raisebox{-4.25ex}{$ x=a $}\sqrt[n]{\raisebox{-4.25ex}{$ 1- {}$}\begin{pmatrix}\dfrac{\sqrt[n]{\dfrac{\sqrt[2-n]{\left(\dfrac{a}
{b}\right)^{2n}}}{\dfrac{1}{a^n}+\dfrac{1}{b^n}\left(\sqrt[2-n]
{\left(\dfrac{a}{b}\right)^{2n}}\right)}}}{\begin{matrix}b \\ \mbox{}\end{matrix}}\end{pmatrix}^n}
\]

\end{document}

Huge white space in fraction

2 Answers2