How to put the numerator in same size as denominator while using brackets

Question

I would like to know how to put the numerator of a fraction of the same size or at least proportional to the denominator when I use square brackets and fractions, as in the following example:

\begin{equation}
\min \left [ \dfrac{1}{\left ( \dfrac{\mu(S) + D_{\psi}(S,\beta) + \xi(S)}{3} \right )} \right ]
\label{eq_1}
\end{equation}

The fraction numerator (1) is very disproportionate (smaller) than the denominator (that contains another fraction)...

Can anybody help me?

Answer 1

As David Carlisle says, the answer is to use \frac instead of \dfrac, which will make the inner denominator fraction shrink appropriately. That's the correct answer to the question, but the question is wrong because the desired result looks poor. A better result is

\begin{equation}
\min \left [ \frac{3}{\mu(S) + D_{\psi}(S,\beta) + \xi(S)} \right ]
\label{eq_1}
\end{equation}

I make this answer not to force a particular style, but to point out that typographic needs come into play and should be given some weight when deciding how to present material. Avoiding tiny text is still important, even when most people read pdfs on screen rather than photocopies on paper. Deeply or asymmetrically nested fractions can often benefit from reformatting -- using mathematical rearrangement, inline "slash" fractions, or the occasional ^{-1} for a reciprocal. Nested exponents or exponents with fractions can benefit from using the \exp function instead of e^.

Answer 2

Some proposals you can choose from.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Original:
\begin{equation}
\min \left [ \dfrac{1}{\left ( \dfrac{\mu(S) + D_{\psi}(S,\beta) + \xi(S)}{3} \right )} \right ]
\label{eq_1}
\end{equation}
Donald's proposal:
\begin{equation}
\min \left [ \frac{3}{\mu(S) + D_{\psi}(S,\beta) + \xi(S)} \right ]
\label{eq_2}
\end{equation}
No brackets:
\begin{equation}
\min \frac{1}{; \dfrac{\mu(S) + D_{\psi}(S,\beta) + \xi(S)}{3};}
\label{eq_3}
\end{equation}
No brackets, smaller denominator:
\begin{equation}
\min \frac{1}{; \frac{\mu(S) + D_{\psi}(S,\beta) + \xi(S)}{3};}
\label{eq_4}
\end{equation}
Reciprocal:
\begin{equation}
\min \left(\frac{\mu(S) + D_{\psi}(S,\beta) + \xi(S)}{3}\right)^{!-1}
\label{eq_5}
\end{equation}
\end{document}

Answer 3

I don't think you really need the brackets, but here are two ways to improve the result with a bmatrix and, in the second example, a medium-sized fraction in the denominator:

\documentclass{article}
\usepackage{nccmath, amsmath}
\begin{document}
\begin{align}
 & \min \begin{bmatrix} \dfrac{1}{\left ( \dfrac{\mu(S) + D_{\psi}(S,\beta) + \xi(S)}{3} \right )}\end{bmatrix} \label{eq_1}\
\intertext{or }
 & \min \begin{bmatrix} \dfrac{1}{ \mfrac{\mu(S) + D_{\psi}(S,\beta) + \xi(S)}{3} } \end{bmatrix}
\label{eq_2}
\end{align}
\end{document}