mjhjmtu

I have created two fractions (see example below), but the denominator is a little too close to the division bar. Can I change this somehow?

documentclassarticle
usepackageamsmath

begindocument
 Combining two Gaussians with mean $mu_1, mu_2$ and variance $sigma_1^2, sigma_2^2$ yields a new Gaussian with mean $mu = fracsigma_2^2 mu_1 + sigma_1^2 mu_2sigma_1^2 + sigma_2^2$ and variance $sigma^2 = frac1frac1sigma_1^2 + frac1sigma_2^2$
enddocument

You have two main options:

• Switch from frac......-notation to inline-fraction notation




• Switch to display math to typeset the formulas for mu and sigma^2.

documentclassarticle
usepackageamsmath % for "text" macro
begindocument

noindent
1. OP's original version:

Combining two Gaussians with mean $mu_1, mu_2$ and variance $sigma_1^2, sigma_2^2$ yields a new Gaussian with mean $mu = fracsigma_2^2 mu_1 + sigma_1^2 mu_2sigma_1^2 + sigma_2^2$ and variance $sigma^2 = frac1frac1sigma_1^2 + frac1sigma_2^2$.

medskipnoindent
2. Partial switch to inline-math notation

Combining two Gaussians with mean $mu_1, mu_2$ and variance 
$sigma_1^2, sigma_2^2$ yields a new Gaussian with mean 
$mu = fracsigma_2^2 mu_1 + sigma_1^2 mu_2sigma_1^2 + sigma_2^2$ 
and variance $sigma^2 = frac11/sigma_1^2 + 1/sigma_2^2$.

medskipnoindent
3. Full switch to inline math notation

Combining two Gaussians with means $mu_1$ and $mu_2$ and 
variances $sigma_1^2$ and $sigma_2^2$ yields a new Gaussian 
with mean $mu = (sigma_2^2 mu_1 + sigma_1^2 mu_2)/(sigma_1^2 + 
sigma_2^2)$ and variance $sigma^2 = 1/(1/sigma_1^2 + 1/sigma_2^2)$.

medskipnoindent
4. Switch to display math

Combining two Gaussians with means $mu_1$ and $mu_2$ and 
variances $sigma_1^2$ and $sigma_2^2$ yields a new Gaussian 
with mean $mu$ and variance $sigma^2$ given by
[
mu=fracsigma_2^2 mu_1 + sigma_1^2 mu_2sigma_1^2 + sigma_2^2 
quadtextandquad 
sigma^2 = frac11/sigma_1^2 + 1/sigma_2^2,.
]

enddocument 

Here, I preserve the fraction in its native textstyle, but add a (default) 1pt buffer above and below the numerator and denominator of each fraction, which can be changed with an optional argument. I call it qfrac. The MWE shows before and after.

documentclassarticle
usepackagestackengine,scalerel
stackMath
newcommandqfrac[3][1pt]frac%
 ThisStyleaddstackgap[#1]SavedStyle#2%
 ThisStyleaddstackgap[#1]SavedStyle#3%

usepackageamsmath

begindocument
 Combining two Gaussians with mean $mu_1, mu_2$ and variance $sigma_1^2, 
 sigma_2^2$ yields a new Gaussian with mean $mu = fracsigma_2^2 mu_1 + 
 sigma_1^2 mu_2sigma_1^2 + sigma_2^2$ and variance $sigma^2 = 
 frac1frac1sigma_1^2 + frac1sigma_2^2$

 Combining two Gaussians with mean $mu_1, mu_2$ and variance $sigma_1^2, 
 sigma_2^2$ yields a new Gaussian with mean $mu = qfracsigma_2^2 mu_1 + 
 sigma_1^2 mu_2sigma_1^2 + sigma_2^2$ and variance $sigma^2 = 
 qfrac[.5pt]1qfrac1sigma_1^2 + qfrac1sigma_2^2$
enddocument