# How can I fix the excessively large subscripts inside a complex nested fraction?

I have an fraction equation; under the denomination, the subscript looks larger than the variables. For example, for a_{GL}, GL looks larger than a. It looks weird. How can I handle this and make the equation look more beautiful? I have tried \dfrac, the equation does not look better. since each term in the denominator has specific physical meaning, I do not want to change formulation of the equation. The picture is attached here.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
This is the reaction equation:
$$\label{eq: rate} r = \frac{P_{A_b}}{\frac{1}{\frac{k_G a_{GL}}{\rho_b \epsilon_s}} + \frac{H}{\frac{k_L a_{GL}}{\rho_b \epsilon_s}} + \frac{H}{\frac{k_{C_A} S_{x}}{{\rho_s V_\rho}}} + \frac{H}{\eta \hat{k} S_g} }$$

\end{document}

• Perhaps you can try adding \displaystyle to the start of the denominator? – MickG Nov 9 '15 at 19:39
• How do you like this? Or perhaps this? – MickG Nov 9 '15 at 19:48

in this case, you might consider a different approach, since the numerator is quite simple:

\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
This is the reaction equation:
$$\label{eq: rate} r = P_{A_b} \bigg/ \! \biggl( \frac{1}{\frac{k_G a_{GL}}{\rho_b \epsilon_s}} + \frac{H}{\frac{k_L a_{GL}}{\rho_b \epsilon_s}} + \frac{H}{\frac{k_{C_A} S_{x}}{{\rho_s V_\rho}}} + \frac{H}{\eta \hat{k} S_g} \biggr)$$

\end{document}


addendum: since it has been pointed out that nobody is addressing the fact that, in the original, the G and L in the subscripts in the denominator fractions are the same size (and look larger, since they're uppercase) than the variables they're subscripted to, here's the explanation.

there are three sizes of fonts in a "default" display: the main size, \scriptstyle and \scriptscriptstyle. in a fraction, the "main size" in the numerator and denominator is \scriptstyle, and the size of sub- and superscripts within the numerator and denominator are the next size down -- which is also the smallest size available. when another fraction is embedded in a numerator or denominator, and that fraction has sub- or superscripts, there's no smaller font to call on. so all glyphs in the "second-order" fraction are set in the same size -- \scriptscriptstyle. therefore, some drastic measures must be taken to make a visible difference.

as recommended when there is a complicated exponential function, rather than setting everything as a superscript, using \exp(...) to bring everything up a size (and make it readable), reformulating a complicated expression such as the one presented in this question is a legitimate way of approaching the problem. the best solution is the one that is least visually confusing as well as mathematically valid, and that's not always accomplished by simply changing the size of all the elements to be in "proper" relative sizes.

Here's a few ways to re-write it that you might consider:

% arara: pdflatex
\documentclass{article}
\usepackage{amsmath}
\begin{document}

$$r = \frac{P_{A_b}}{H\left(\frac{1}{\frac{Hk_G a_{GL}}{\rho_b \epsilon_s}} + \frac{1}{\frac{k_L a_{GL}}{\rho_b \epsilon_s}} + \frac{1}{\frac{k_{C_A} S_{x}}{{\rho_s V_\rho}}} + \frac{1}{\eta \hat{k} S_g} \right)}$$

$$r = \frac{P_{A_b}}{H\left(\frac{\rho_b \epsilon_s}{Hk_G a_{GL}} + \frac{\rho_b \epsilon_s}{k_L a_{GL}} + \frac{{\rho_s V_\rho}}{k_{C_A} S_{x}} + \frac{1}{\eta \hat{k} S_g} \right)}$$

$$r = \frac{P_{A_b}}{H}\left(\frac{\rho_b \epsilon_s}{Hk_G a_{GL}} + \frac{\rho_b \epsilon_s}{k_L a_{GL}} + \frac{{\rho_s V_\rho}}{k_{C_A} S_{x}} + \frac{1}{\eta \hat{k} S_g} \right)^{-1}$$
\end{document}


Try

$$\label{eq: rate} r = \frac{P_{A_b}} {\dfrac{1}{\dfrac{k_G a_{GL}}{\rho_b \epsilon_s}} + \dfrac{H}{\dfrac{k_L a_{GL}}{\rho_b \epsilon_s}} + \dfrac{H}{\dfrac{k_{C_A} S_{x}}{{\rho_s V_\rho}}} + \dfrac{H}{\eta \hat{k} S_g} }$$
\end{document}


if it is what you looking for.

Further improvements: As pointed egreg in his comment, further refinement can be obtain with writing variable with only subscripts for example as $k^{}_G$. With this subscripts is moved slightly down and are aligned with subscripts at variable which has some exponent.

If the sub- and sup- scripts are simple (for example not fractions), simalar results gives use of package subdepth with option low-sup:

\documentclass{article}
\usepackage{amsmath}
\usepackage[low-sup]{subdepth}

\begin{document}
$$\label{eq: rate} r = \frac{P_{A_b}} {\dfrac{1}{\dfrac{k_G a_{GL}}{\rho_b \epsilon_s}} + \dfrac{H}{\dfrac{k_L a_{GL}}{\rho_b \epsilon_s}} + \dfrac{H}{\dfrac{k_{C_A} S_{x}}{{\rho_s V_\rho}}} + \dfrac{H}{\eta \hat{k} S_g} }$$
\end{document}


With this package the equation looks as follows:

• A good refinement would be adding ^{} where there are uppercase subscripts, so k^{}_{G} and similarly in the next terms. – egreg Nov 9 '15 at 16:44
• Yes, of course. Similar refinements can be achieved )at simple exponents and indices) width adding of the package subdepth with option  low-sup in preamble. – Zarko Nov 9 '15 at 17:00

How about the following expression? It (a) uses inverses of parenthetical expressions instead of compound fractions, (b) uses ^{} terms to force the subscripts to be placed a bit lower than would otherwise be the case, and (c) factors out the term H that's present in all three remaining fractional terms.

With this setup, the base variables -- k and a -- are typeset in what's called scriptstyle and the subscripts -- L and GL among them -- are typeset in scriptscriptstyle, which is 30% smaller than scriptstyle. With these relative sizes, and especially if you use the ^{} device mentioned in item (b) above, it should be no problem to distinguish visually between base- and subscript-level variables.

(Naturally, the inverted parenthetical expressions can be inverted once more, giving you the final expression in @cmhughes' answer.)

\documentclass{article}
\begin{document}
This is the reaction equation:
$$\label{eq: rate} r = P^{}_{A_b} H^{-1} \biggl[ \biggl( H\frac{k^{}_G a^{}_{GL}}{\rho^{}_b \epsilon^{}_s} \biggr)^{\!-1} + \biggl( \frac{k^{}_L a^{}_{GL}}{\rho^{}_b \epsilon^{}_s} \biggr)^{\!-1} + \biggl( \frac{k^{}_{C_A} S^{}_{x}}{\rho^{}_s V^{}_\rho} \biggr)^{\!-1} + \Bigl( \eta \hat{k} S^{}_g \Bigr)^{\!-1} \, \biggr]^{-1}$$
\end{document}